Finite Group Databasebeta

← #11778589

Subgroups — #11778589

Order 1152.

495 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 495 conjugacy classes of subgroups — too many to draw. Only its 80 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#10594813C211yesmaximal, characteristic
2#10592682C211yesmaximal, characteristic
3C3×#4971C212yesmaximal
4#10589152C212yesmaximal
5#10589148C211yesmaximal, characteristic
6#71175—32nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×#3750—21no—
9C2×#3750C2211yescharacteristic
10C3×#924C2212yes—
11#63982—21no—
12#63957—21no—
13#63847—22no—
14#63839—22no—
15#63658—21no—
16#63658C2211yescharacteristic
17C3×#830C2212yes—
18C3×#810—22no—
19C3×#808—22no—
20#5623—32no—
21C3×#483—32no—
22#4983—32no—
23#4983—61no—
24#4971D312yes—
25#4538—32no—
26#4469—32no—
27#4467—32no—
28C22×C32×C4—21no—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C2×C3×Dic6D412yes—
34C2×#627—21no—
35C32×C4⋊C4—22no—
36#3750—22no—
37#3750—42no—
38C3×#217—22no—
39C3×C4⋊Dic3D412yes—
40C3×Dic3⋊C4—22no—
41C2×C3×C3⋊C8—22no—
42#3724—21no—
43#3724—21no—
44#3724—21no—
45Dic3⋊Dic3—22no—
46Dic32—22no—
47#1611—91noSylow
48C3×C22⋊Q8—32no—
49C2×C3×C4⋊C4—21no—
50C2×C3×C4⋊C4C2×D312yes—
51#944—62no—
52#924C2×D312yes—
53C2×Dic3⋊C4—32no—
54C2×Dic3⋊C4—61no—
55C2×Dic3⋊C4—62no—
56C2×Dic3⋊C4—62no—
57#889—62no—
58#889—62no—
59#888—62no—
60#878—62no—
61#877—62no—
62C3×#106—62no—
63C3×#103—62no—
64C3×C22⋊C8—32no—
65C3⋊#95—32no—
66C3⋊#95—61no—
67C3⋊#95—62no—
68C3⋊#95—62no—
69#830C2×D312yes—
70#810—22no—
71#808—22no—
72C23×C32C2×D411yescharacteristic
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C32×C4—41no—
77C2×C32×C4C2×D412yes—
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3—21no—
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—41no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3SD1612yes—
86C2×C3×Dic3—22no—
87C2×C3×Dic3—22no—
88C3×Dic6—42no—
89#627—81no—
90C3×C3⋊C8—42no—
91#544—91no—
92#483—32no—
93#398—91no—
94#328—92no—
95#324—91no—
96C2×C3×Q8—32no—
97C22×C3×C4—22no—
98C22×C3×C4—22no—
99C22×C3×C4—21no—
100C22×C3×C4C22×D312yes—
101C22×Dic3—32no—
102C22×Dic3—32no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—62no—
106C22×Dic3—62no—
107C2×Dic6—62no—
108C2×Dic6#6712yes—
109C2×C3×C8—62no—
110C3×C4⋊C4—22no—
111C3×C4⋊C4—22no—
112C3×C4⋊C4—32no—
113C3×C4⋊C4—42no—
114C3×C4⋊C4—62no—
115C3×C22⋊C4—62no—
116#217—22no—
117C4⋊Dic3—62no—
118C4⋊Dic3#6712yes—
119Dic3⋊C4—22no—
120Dic3⋊C4—62no—
121Dic3⋊C4—62no—
122Dic3⋊C4—62no—
123Dic3⋊C4—62no—
124Dic3⋊C4—62no—
125Dic3⋊C4—62no—
126Dic3⋊C4—122no—
127Dic3⋊C4—124no—
128Dic3⋊C4—124no—
129C4×Dic3—62no—
130C4×Dic3—62no—
131C2×C3⋊C8—22no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32#12011yescharacteristic
135C22×C32C2×SD1611yescharacteristic
136C22×C32#13711yescharacteristic
137C32×C4—22no—
138C32×C4—81no—
139C3⋊Dic3—22no—
140C3⋊Dic3—42no—
141C3⋊Dic3—41no—
142C3×Dic3—42no—
143C3×Dic3—42no—
144C4⋊Q8—182no—
145#125—182no—
146C22⋊Q8—32no—
147C22⋊Q8—181no—
148#117—181no—
149C2×C4⋊C4—91no—
150C2×C4⋊C4—181no—
151C2×C4⋊C4D3211yescharacteristic
152#106—62no—
153#103—62no—
154C22⋊C8—32no—
155#95—91no—
156#95—181no—
157C23×C3—21no—
158C23×C3D3×D412yes—
159C3×Q8—122no—
160C2×C3×C4—22no—
161C2×C3×C4—42no—
162C2×C3×C4—42no—
163C2×C3×C4—42no—
164C2×C3×C4—42no—
165C2×C3×C4—42no—
166C2×C3×C4—42no—
167C2×C3×C4—42no—
168C2×C3×C4—42no—
169C2×C3×C4—62no—
170C2×C3×C4—62no—
171C2×C3×C4D3×D412yes—
172C2×C3×C4C2×#6712yes—
173C2×Dic3—22no—
174C2×Dic3—22no—
175C2×Dic3—34no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C2×Dic3—62no—
179C2×Dic3—64no—
180C2×Dic3—64no—
181C2×Dic3—62no—
182C2×Dic3—121no—
183C2×Dic3—121no—
184C2×Dic3—121no—
185C2×Dic3—122no—
186C2×Dic3—122no—
187C2×Dic3—122no—
188C2×Dic3—122no—
189C2×Dic3—122no—
190C2×Dic3—122no—
191Dic6—42no—
192Dic6—242no—
193C3×C8—122no—
194C3⋊C8—42no—
195C2×C32—21no—
196C2×C32—21no—
197C2×C32#44811yescharacteristic
198C2×C32#45611yescharacteristic
199C2×C32#45811yescharacteristic
200C2×Q8—32no—
201C2×Q8—181no—
202C22×C4—21no—
203C22×C4—91no—
204C22×C4—91no—
205C22×C4—181no—
206C22×C4C2×D3211yescharacteristic
207C2×C8—62no—
208C4⋊C4—22no—
209C4⋊C4—32no—
210C4⋊C4—62no—
211C4⋊C4—181no—
212C4⋊C4—181no—
213C4⋊C4—181no—
214C4⋊C4—182no—
215C4⋊C4—182no—
216C4⋊C4—362no—
217C22⋊C4—62no—
218C42—182no—
219C22×C3—22no—
220C22×C3—22no—
221C22×C3—22no—
222C22×C3—22no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3D3×SD1612yes—
227C22×C3#91512yes—
228C22×C3#93712yes—
229C3×C4—22no—
230C3×C4—22no—
231C3×C4—42no—
232C3×C4—82no—
233C3×C4—82no—
234C3×C4—122no—
235C3×C4—122no—
236Dic3—42no—
237Dic3—42no—
238Dic3—64no—
239Dic3—122no—
240Dic3—124no—
241Dic3—124no—
242Dic3—122no—
243Dic3—241no—
244C32#161111yescharacteristic, complemented, Sylow
245C23#381111yescharacteristic
246Q8—122no—
247Q8—721no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—62no—
253C2×C4—62no—
254C2×C4—92no—
255C2×C4—181no—
256C2×C4—181no—
257C2×C4—182no—
258C2×C4—181no—
259C2×C4—361no—
260C2×C4—361no—
261C2×C4—361no—
262C2×C4D3×#6712yes—
263C8—122no—
264C2×C3—22no—
265C2×C3—22no—
266C2×C3—22no—
267C2×C3—22no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3#505312yes—
272C2×C3#517012yes—
273C2×C3#520512yes—
274C22—21no—
275C22—21no—
276C22#6393011yescharacteristic
277C22#6393111yescharacteristic
278C22#6398311yescharacteristic
279C4—22no—
280C4—81no—
281C4—122no—
282C4—122no—
283C4—182no—
284C4—362no—
285C4—361no—
286C3—21no—
287C3#7117512yescomplemented
288C2—21no—
289C2—21no—
290C2#1059139811yescharacteristic
291C2#1059151811yescharacteristic
292C2#1059166011yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#1611
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
244. C32#1611semidirect
287. C3#71175semidirect

Maximal subgroups

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

subgroupindex
#105948132
#105926822
C3×#49712
#105891522
#105891482
#711753