Finite Group Databasebeta

← #11794259

Subgroups — #11794259

Order 1152.

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

normal subgroups only

This group has 585 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#10592634C211yesmaximal, characteristic
3#10591131C212yesmaximal
4C3×#4523C212yesmaximal
5#10589168C211yesmaximal, characteristic
6#68735—32nomaximal
7C2×C32×C42C2211yescharacteristic
8C2×C4⋊(C3⋊Dic3)—22no—
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C3×#926C2212yes—
12C2×C3×#208C2212yes—
13#63982—22no—
14#63918—22no—
15#63869—22no—
16#63575—22no—
17#63573—22no—
18#5519—32no—
19#5121—32no—
20#4995—32no—
21#4935—32no—
22#4935—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—
35C4⋊(C3⋊Dic3)—44no—
36C3×#217—22no—
37C3×C4⋊Dic3D412yes—
38C3×C4⋊Dic3D412yes—
39C3×C4×Dic3—22no—
40C3×#208—22no—
41C3×#208Q814yescomplemented
42C2×C3×C3⋊C8—22no—
43#3724—22no—
44Dic3⋊Dic3—24no—
45#2060—91noSylow
46C2×C3×M16—32no—
47C3×#117—32no—
48C2×C3×C42—21no—
49C2×C3×C42C2×D312yes—
50#926C2×D312yes—
51C2×C4⋊Dic3—32no—
52C2×C4⋊Dic3—32no—
53C2×C4⋊Dic3—61no—
54C2×C4⋊Dic3—61no—
55C2×C4⋊Dic3—64no—
56C2×C4⋊Dic3—64no—
57C2×#208C2×D312yes—
58#890—62no—
59#888—62no—
60#878—64no—
61#870—62no—
62#869—62no—
63#818—62no—
64#817—62no—
65#808—62no—
66#807—62no—
67C23×C32C2×D411yescharacteristic
68C2×C32×C4—22no—
69C2×C32×C4—22no—
70C2×C32×C4—22no—
71C2×C32×C4C2×D412yes—
72C2×C32×C4C2×Q811yescharacteristic
73C2×C32×C4C2×Q812yes—
74C2×C32×C4#4111yescharacteristic
75C2×C3⋊Dic3—22no—
76C2×C3⋊Dic3—42no—
77C2×C3⋊Dic3—42no—
78C2×C3⋊Dic3—41no—
79C2×C3×Dic3—22no—
80C2×C3×Dic3—22no—
81#627—82no—
82C3×C3⋊C8—24no—
83#544—91no—
84#428—92no—
85#384—91no—
86#343—91no—
87#339—32no—
88C22×C3×C4—22no—
89C22×C3×C4—22no—
90C22×C3×C4—21no—
91C22×C3×C4C22×D312yes—
92C22×Dic3—34no—
93C22×Dic3—62no—
94C22×Dic3—62no—
95C22×Dic3—62no—
96C2×Dic6—64no—
97C3×M16—34no—
98C3×M16—62no—
99C2×C3×C8—62no—
100C3×C4⋊C4—32no—
101C3×C4⋊C4—32no—
102C3×C22⋊C4—62no—
103C3×C42—22no—
104C3×C42—22no—
105C3×C42—22no—
106C3×C42—62no—
107C3×C42Dic614yescomplemented
108#217—22no—
109C4⋊Dic3—64no—
110C4⋊Dic3—62no—
111C4⋊Dic3—62no—
112C4⋊Dic3—62no—
113C4⋊Dic3—62no—
114C4⋊Dic3—122no—
115C4⋊Dic3—122no—
116C4⋊Dic3—128no—
117C4⋊Dic3—128no—
118C4⋊Dic3D1212yes—
119C4⋊Dic3D1212yes—
120Dic3⋊C4—64no—
121Dic3⋊C4—64no—
122C4×Dic3—22no—
123#208—22no—
124#208Dic614yescomplemented
125C2×C3⋊C8—22no—
126C22×C32—21no—
127C22×C32—21no—
128C22×C32#12011yescharacteristic
129C22×C32C22⋊Q811yescharacteristic
130C22×C32C4⋊Q811yescharacteristic
131C32×C4—24no—
132C32×C4C22⋊Q812yes—
133C32×C4C4⋊Q812yes—
134C3⋊Dic3—42no—
135C3⋊Dic3—81no—
136C3×Dic3—42no—
137C3×Dic3—42no—
138C2×M16—32no—
139C4⋊Q8—182no—
140#125—182no—
141C22⋊Q8—182no—
142#117—32no—
143C2×C4⋊C4—91no—
144C2×C4⋊C4—91no—
145C2×C4⋊C4—182no—
146C2×C42D3211yescharacteristic
147#107—182no—
148#106—182no—
149C23×C3—21no—
150C23×C3D3×D412yes—
151C2×C3×C4—24no—
152C2×C3×C4—24no—
153C2×C3×C4—24no—
154C2×C3×C4—24no—
155C2×C3×C4—24no—
156C2×C3×C4—24no—
157C2×C3×C4—22no—
158C2×C3×C4—22no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—62no—
162C2×C3×C4—62no—
163C2×C3×C4C2×Dic612yes—
164C2×C3×C4C2×Dic612yes—
165C2×C3×C4C2×D1212yes—
166C2×C3×C4D3×D412yes—
167C2×C3×C4#23712yes—
168C2×C3×C4D3×Q812yes—
169C2×Dic3—22no—
170C2×Dic3—22no—
171C2×Dic3—64no—
172C2×Dic3—122no—
173C2×Dic3—124no—
174C2×Dic3—124no—
175C2×Dic3—124no—
176C2×Dic3—124no—
177C2×Dic3—122no—
178C2×Dic3—122no—
179Dic6—244no—
180C3×C8—64no—
181C3⋊C8—24no—
182C2×C32—21no—
183C2×C32—21no—
184C2×C32#39511yescharacteristic
185C2×C32#45311yescharacteristic
186C2×C32#45611yescharacteristic
187C2×Q8—182no—
188C22×C4—21no—
189C22×C4—92no—
190C22×C4—181no—
191C22×C4C2×D3211yescharacteristic
192M16—34no—
193M16—62no—
194C2×C8—62no—
195C4⋊C4—32no—
196C4⋊C4—32no—
197C4⋊C4—182no—
198C4⋊C4—184no—
199C4⋊C4—182no—
200C4⋊C4—182no—
201C4⋊C4—364no—
202C22⋊C4—62no—
203C42—21no—
204C42—62no—
205C42#62712yescomplemented
206C22×C3—22no—
207C22×C3—22no—
208C22×C3—22no—
209C22×C3—22no—
210C22×C3—21no—
211C22×C3—21no—
212C22×C3—21no—
213C22×C3#87812yes—
214C22×C3#88212yes—
215C22×C3#88812yes—
216C3×C4—28no—
217C3×C4—28no—
218C3×C4—22no—
219C3×C4—22no—
220C3×C4—122no—
221C3×C4—122no—
222C3×C4#86912yes—
223C3×C4#87812yes—
224C3×C4#88812yes—
225C3×C4#89712yes—
226Dic3—42no—
227Dic3—42no—
228Dic3—124no—
229Dic3—242no—
230Dic3—242no—
231Dic3—242no—
232C32#206011yescharacteristic, complemented, Sylow
233C23#381111yescharacteristic
234Q8—722no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—62no—
239C2×C4—62no—
240C2×C4—182no—
241C2×C4—362no—
242C2×C4—362no—
243C2×C4—361no—
244C2×C4D3×Dic612yes—
245C2×C4D3×D1212yes—
246C2×C4#380511yescharacteristic
247C2×C4C2×#62711yescharacteristic
248C8—64no—
249C2×C3—22no—
250C2×C3—22no—
251C2×C3—22no—
252C2×C3—22no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3#465612yes—
257C2×C3#482212yes—
258C2×C3#482612yes—
259C22—21no—
260C22—21no—
261C22#6384011yescharacteristic
262C22#6392311yescharacteristic
263C22#6398211yescharacteristic
264C4—24no—
265C4—122no—
266C4—122no—
267C4—362no—
268C4—721no—
269C4#6389312yes—
270C4#6391812yes—
271C3—21no—
272C3#6873512yescomplemented
273C2—21no—
274C2—21no—
275C2#1059039711yescharacteristic
276C2#1059040111yescharacteristic
277C2#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#2060
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
41. C3×#208Q8semidirect
107. C3×C42Dic6semidirect
124. #208Dic6semidirect
205. C42#627semidirect
232. C32#2060semidirect
272. C3#68735semidirect

Maximal subgroups

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

subgroupindex
#105950522
#105926342
#105911312
C3×#45232
#105891682
#687353