Finite Group Databasebeta

← #11794292

Subgroups — #11794292

Order 1152.

537 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 537 conjugacy classes of subgroups — too many to draw. Only its 126 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#10595052C211yesmaximal, characteristic
2#10592635C211yesmaximal, characteristic
3#10591131C212yesmaximal
4C3×#4523C212yesmaximal
5#10589168C211yesmaximal, characteristic
6#68736—32nomaximal
7C2×C32×C42C2211yescharacteristic
8C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C3×#926C2212yes—
11C2×C3×#208C2212yes—
12#63982—22no—
13#63918—22no—
14#63869—22no—
15#63658—22no—
16#63575—22no—
17#63573—22no—
18#5519—32no—
19#5121—32no—
20#4995—32no—
21#4936—32no—
22#4936—61no—
23C3×#339—32no—
24#4554—32no—
25#4523D312yes—
26C22×C32×C4—21no—
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3—21no—
29C22×C3⋊Dic3D412yes—
30C2×#627—22no—
31C32×C42—21no—
32C32×C42Q812yescomplemented
33C4⋊(C3⋊Dic3)—22no—
34C4⋊(C3⋊Dic3)—22no—
35C3×#217—22no—
36C3×C4⋊Dic3D412yes—
37C3×C4⋊Dic3D412yes—
38C3×C4×Dic3—22no—
39C3×#208—22no—
40C3×#208Q814yescomplemented
41C2×C3×C3⋊C8—22no—
42#3724—22no—
43Dic3⋊Dic3—24no—
44#2061—91noSylow
45C2×C3×M16—32no—
46C3×#117—32no—
47C2×C3×C42—21no—
48C2×C3×C42C2×D312yes—
49#926C2×D312yes—
50C2×C4⋊Dic3—32no—
51C2×C4⋊Dic3—32no—
52C2×C4⋊Dic3—61no—
53C2×C4⋊Dic3—61no—
54C2×#208C2×D312yes—
55#890—62no—
56#888—62no—
57#878—64no—
58#870—62no—
59#869—62no—
60C3⋊#95—64no—
61C3⋊#95—64no—
62#818—62no—
63#817—62no—
64#808—62no—
65#807—62no—
66C23×C32C2×D411yescharacteristic
67C2×C32×C4—22no—
68C2×C32×C4—41no—
69C2×C32×C4—41no—
70C2×C32×C4C2×D412yes—
71C2×C32×C4C2×Q811yescharacteristic
72C2×C32×C4C2×Q812yes—
73C2×C32×C4#4111yescharacteristic
74C2×C3⋊Dic3—22no—
75C2×C3⋊Dic3—42no—
76C2×C3⋊Dic3—42no—
77C2×C3⋊Dic3—41no—
78C2×C3×Dic3—22no—
79C2×C3×Dic3—22no—
80#627—82no—
81C3×C3⋊C8—24no—
82#544—91no—
83#428—92no—
84#382—91no—
85#343—91no—
86#339—32no—
87C22×C3×C4—22no—
88C22×C3×C4—22no—
89C22×C3×C4—21no—
90C22×C3×C4C22×D312yes—
91C22×Dic3—34no—
92C22×Dic3—62no—
93C22×Dic3—62no—
94C22×Dic3—62no—
95C2×Dic6—64no—
96C3×M16—34no—
97C3×M16—62no—
98C2×C3×C8—62no—
99C3×C4⋊C4—32no—
100C3×C4⋊C4—32no—
101C3×C22⋊C4—62no—
102C3×C42—22no—
103C3×C42—22no—
104C3×C42—22no—
105C3×C42—62no—
106C3×C42Dic614yescomplemented
107#217—22no—
108C4⋊Dic3—64no—
109C4⋊Dic3—62no—
110C4⋊Dic3—62no—
111C4⋊Dic3—62no—
112C4⋊Dic3—62no—
113C4⋊Dic3—122no—
114C4⋊Dic3—122no—
115C4⋊Dic3D1212yes—
116C4⋊Dic3D1212yes—
117Dic3⋊C4—64no—
118Dic3⋊C4—64no—
119C4×Dic3—22no—
120#208—22no—
121#208Dic614yescomplemented
122C2×C3⋊C8—22no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32#12011yescharacteristic
126C22×C32C22⋊Q811yescharacteristic
127C22×C32C4⋊Q811yescharacteristic
128C32×C4—42no—
129C32×C4C22⋊Q812yes—
130C32×C4C4⋊Q812yes—
131C3⋊Dic3—42no—
132C3⋊Dic3—81no—
133C3×Dic3—42no—
134C3×Dic3—42no—
135C2×M16—32no—
136C4⋊Q8—182no—
137#125—182no—
138C22⋊Q8—182no—
139#117—32no—
140C2×C4⋊C4—91no—
141C2×C4⋊C4—91no—
142C2×C42D3211yescharacteristic
143#107—182no—
144#106—182no—
145#95—182no—
146C23×C3—21no—
147C23×C3D3×D412yes—
148C2×C3×C4—24no—
149C2×C3×C4—24no—
150C2×C3×C4—22no—
151C2×C3×C4—22no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—42no—
155C2×C3×C4—42no—
156C2×C3×C4—42no—
157C2×C3×C4—42no—
158C2×C3×C4—62no—
159C2×C3×C4—62no—
160C2×C3×C4C2×Dic612yes—
161C2×C3×C4C2×Dic612yes—
162C2×C3×C4C2×D1212yes—
163C2×C3×C4D3×D412yes—
164C2×C3×C4#23712yes—
165C2×C3×C4D3×Q812yes—
166C2×Dic3—22no—
167C2×Dic3—22no—
168C2×Dic3—64no—
169C2×Dic3—122no—
170C2×Dic3—124no—
171C2×Dic3—122no—
172C2×Dic3—124no—
173C2×Dic3—124no—
174C2×Dic3—124no—
175C2×Dic3—122no—
176Dic6—244no—
177C3×C8—64no—
178C3⋊C8—24no—
179C2×C32—21no—
180C2×C32—21no—
181C2×C32#39511yescharacteristic
182C2×C32#45411yescharacteristic
183C2×C32#45511yescharacteristic
184C2×Q8—182no—
185C22×C4—21no—
186C22×C4—92no—
187C22×C4—181no—
188C22×C4C2×D3211yescharacteristic
189M16—34no—
190M16—62no—
191C2×C8—62no—
192C4⋊C4—32no—
193C4⋊C4—32no—
194C4⋊C4—182no—
195C4⋊C4—184no—
196C4⋊C4—182no—
197C4⋊C4—182no—
198C22⋊C4—62no—
199C42—21no—
200C42—62no—
201C42#62712yescomplemented
202C22×C3—22no—
203C22×C3—22no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—21no—
207C22×C3—21no—
208C22×C3—21no—
209C22×C3#87812yes—
210C22×C3#88212yes—
211C22×C3#88812yes—
212C3×C4—22no—
213C3×C4—22no—
214C3×C4—44no—
215C3×C4—44no—
216C3×C4—122no—
217C3×C4—122no—
218C3×C4#86912yes—
219C3×C4#87812yes—
220C3×C4#88812yes—
221C3×C4#89712yes—
222Dic3—42no—
223Dic3—42no—
224Dic3—124no—
225Dic3—242no—
226Dic3—242no—
227Dic3—242no—
228C32#206111yescharacteristic, complemented, Sylow
229C23#381111yescharacteristic
230Q8—722no—
231C2×C4—22no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—62no—
235C2×C4—62no—
236C2×C4—182no—
237C2×C4—362no—
238C2×C4—362no—
239C2×C4—361no—
240C2×C4D3×Dic612yes—
241C2×C4D3×D1212yes—
242C2×C4#380511yescharacteristic
243C2×C4C2×#62711yescharacteristic
244C8—64no—
245C2×C3—22no—
246C2×C3—22no—
247C2×C3—22no—
248C2×C3—22no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3#465612yes—
253C2×C3#482512yes—
254C2×C3#482712yes—
255C22—21no—
256C22—21no—
257C22#6384011yescharacteristic
258C22#6392311yescharacteristic
259C22#6398211yescharacteristic
260C4—42no—
261C4—122no—
262C4—122no—
263C4—362no—
264C4—721no—
265C4#6389312yes—
266C4#6391812yes—
267C3—21no—
268C3#6873612yescomplemented
269C2—21no—
270C2—21no—
271C2#1059039811yescharacteristic
272C2#1059040211yescharacteristic
273C2#1059139711yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C42D32
hypocenterC32#2061
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
32. C32×C42Q8semidirect
40. C3×#208Q8semidirect
106. C3×C42Dic6semidirect
121. #208Dic6semidirect
201. C42#627semidirect
228. C32#2061semidirect
268. C3#68736semidirect

Maximal subgroups

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

subgroupindex
#105950522
#105926352
#105911312
C3×#45232
#105891682
#687363