Finite Group Databasebeta

← #11790472

Subgroups — #11790472

Order 1152.

457 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 457 conjugacy classes of subgroups — too many to draw. Only its 132 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#10592821C211yesmaximal, characteristic
2C2×#63578C211yesmaximal, characteristic
3#10591130C212yesmaximal
4C2×#63574C211yesmaximal, characteristic
5C3×#4554C212yesmaximal
6#68984—32nomaximal
7C2×C32×M16C2211yescharacteristic
8#64135C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4⋊Dic3C2212yes—
11C2×C3×#208C2212yes—
12#63642—21no—
13C8×C3⋊Dic3—21no—
14#63578C414yescomplemented
15#63575—22no—
16#63574—21no—
17#63574—21no—
18#63573—22no—
19C2×#822—32no—
20#5122—32no—
21#5122—61no—
22#5121—32no—
23#4964—32no—
24C2×#808—32no—
25C3×#343—32no—
26#4554D312yes—
27C22×C32×C4C2311yescharacteristic
28C22×C3×Dic3—22no—
29C32×M16—21no—
30C32×M16Q812yes—
31C2×C32×C8—21no—
32#3757—21no—
33C4⋊(C3⋊Dic3)D412yes—
34C4×C3⋊Dic3—21no—
35C2×C3⋊(C3⋊C8)C2×C412yes—
36C2×C3⋊(C3⋊C8)D411yescharacteristic
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38C2×C3⋊(C3⋊C8)Q812yes—
39C3×C4⋊Dic3—22no—
40C3×C4⋊Dic3—22no—
41C3×#208—22no—
42C3×#208C2×C414yes—
43C2×C3×C3⋊C8—22no—
44#1951—91noSylow
45C2×C3×M16—21no—
46C2×C3×M16—32no—
47C2×C3×M16C2×D312yes—
48C2×C3×C4⋊C4—32no—
49#926—32no—
50#926—61no—
51C2×C4⋊Dic3C2×D312yes—
52C2×#208C2×D312yes—
53C22×C3⋊C8—32no—
54C22×C3⋊C8—61no—
55#822—38no—
56#818—62no—
57#817—62no—
58#815—62no—
59#815—62no—
60C8×Dic3—62no—
61C8×Dic3—62no—
62#808—62no—
63#808—62no—
64#808—62no—
65#807—62no—
66C23×C32#4111yescharacteristic
67C2×C32×C4C22×C411yescharacteristic
68C2×C32×C4C2×D411yescharacteristic
69C2×C32×C4C2×D411yescharacteristic
70C2×C32×C4C2×Q811yescharacteristic
71C2×C32×C4C2×Q811yescharacteristic
72C2×C32×C4#4111yescharacteristic
73C2×C3⋊Dic3—22no—
74C2×C3×Dic3—42no—
75C2×C3×Dic3—82no—
76C32×C8—22no—
77C3⋊(C3⋊C8)C4⋊C412yes—
78C3⋊(C3⋊C8)C4⋊C412yes—
79C3×C3⋊C8—24no—
80C2×#108—91no—
81#428—92no—
82C2×#106—91no—
83#405—91no—
84#343—32no—
85C22×C3×C4—21no—
86C22×C3×C4—62no—
87C22×C3×C4C22×D312yes—
88C22×Dic3—22no—
89C3×M16—22no—
90C3×M16—22no—
91C3×M16—22no—
92C3×M16—34no—
93C3×M16—62no—
94C3×M16Dic614yes—
95C2×C3×C8—22no—
96C2×C3×C8—22no—
97C2×C3×C8—62no—
98C3×C4⋊C4—62no—
99C3×C4⋊C4—62no—
100#217—62no—
101#217—62no—
102C4⋊Dic3—22no—
103C4⋊Dic3—22no—
104C4⋊Dic3—32no—
105C4⋊Dic3—32no—
106C4⋊Dic3—62no—
107C4×Dic3—62no—
108C4×Dic3—62no—
109#208—22no—
110#208C4×D314yes—
111C2×C3⋊C8—22no—
112C2×C3⋊C8—34no—
113C2×C3⋊C8—32no—
114C2×C3⋊C8—32no—
115C2×C3⋊C8—34no—
116C2×C3⋊C8—61no—
117C2×C3⋊C8—61no—
118C2×C3⋊C8—62no—
119C2×C3⋊C8—62no—
120C22×C32—22no—
121C22×C32C4×Q811yescharacteristic
122C22×C32#12111yescharacteristic
123C22×C32#12511yescharacteristic
124C32×C4C2×C4⋊C411yescharacteristic
125C32×C4C4×D411yescharacteristic
126C32×C4C22⋊Q811yescharacteristic
127C32×C4C4⋊Q811yescharacteristic
128C3⋊Dic3—42no—
129C3×Dic3—82no—
130C2×M16—32no—
131C2×M16D3211yescharacteristic
132C22×C8—91no—
133#117—91no—
134C2×C4⋊C4—32no—
135#108—94no—
136#107—182no—
137#106—181no—
138#106—181no—
139#106—182no—
140#97—181no—
141C4×C8—181no—
142C23×C3—21no—
143C23×C3#23512yes—
144C2×C3×C4—21no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—122no—
151C2×C3×C4—242no—
152C2×C3×C4C2×Dic612yes—
153C2×C3×C4C2×C4×D312yes—
154C2×C3×C4D3×D412yes—
155C2×C3×C4D3×D412yes—
156C2×C3×C4#23712yes—
157C2×C3×C4D3×Q812yes—
158C2×Dic3—42no—
159C2×Dic3—64no—
160C2×Dic3—62no—
161C2×Dic3—62no—
162C2×Dic3—82no—
163C3×C8—24no—
164C3×C8—24no—
165C3×C8—64no—
166C3⋊C8—24no—
167C3⋊C8—34no—
168C3⋊C8—34no—
169C3⋊C8—62no—
170C3⋊C8—62no—
171C2×C32—21no—
172C2×C32—21no—
173C2×C32#38911yescharacteristic
174C2×C32#47112yes—
175C22×C4—62no—
176C22×C4C2×D3211yescharacteristic
177M16—21no—
178M16—34no—
179M16—62no—
180M16#62712yes—
181C2×C8—21no—
182C2×C8—62no—
183C2×C8—92no—
184C2×C8—92no—
185C2×C8—91no—
186C2×C8—91no—
187C4⋊C4—62no—
188C4⋊C4—62no—
189C4⋊C4—92no—
190C22⋊C4—181no—
191C42—181no—
192C22×C3—22no—
193C22×C3—22no—
194C22×C3—21no—
195C22×C3—21no—
196C22×C3—21no—
197C22×C3—42no—
198C22×C3C4×Dic612yes—
199C22×C3#88412yes—
200C22×C3#88912yes—
201C3×C4—21no—
202C3×C4—21no—
203C3×C4—21no—
204C3×C4—21no—
205C3×C4—242no—
206C3×C4#87812yes—
207C3×C4#67⋊C412yes—
208C3×C4#88812yes—
209C3×C4D3×C4⋊C412yes—
210Dic3—82no—
211Dic3—124no—
212Dic3—122no—
213Dic3—122no—
214C32#195111yescharacteristic, complemented, Sylow
215C23#379811yescharacteristic
216C2×C4—122no—
217C2×C4—182no—
218C2×C4—242no—
219C2×C4#379711yescharacteristic
220C2×C4C4×D3211yescharacteristic
221C2×C4#380211yescharacteristic
222C2×C4#380511yescharacteristic
223C2×C4C2×#62711yescharacteristic
224C2×C4#381111yescharacteristic
225C8—22no—
226C8—64no—
227C8—92no—
228C8—92no—
229C2×C3—22no—
230C2×C3—22no—
231C2×C3—22no—
232C2×C3—21no—
233C2×C3—41no—
234C2×C3—41no—
235C2×C3#464712yes—
236C2×C3#474812yes—
237C2×C3#475412yes—
238C22—22no—
239C22#6387011yescharacteristic
240C22#6391211yescharacteristic
241C22C4×#62711yescharacteristic
242C4—242no—
243C4—362no—
244C4#6388311yescharacteristic
245C4#6390211yescharacteristic
246C4#6391911yescharacteristic
247C4#6398211yescharacteristic
248C3—21no—
249C3#6898412yescomplemented
250C2—21no—
251C2—21no—
252C2#1059099112yes—
253C2#1059132811yescharacteristic
subgroupG/H
centerC22#63912
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC23×C32#41
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1951
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
14. #63578C4semidirect
214. C32#1951semidirect
249. C3#68984semidirect

Maximal subgroups

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

subgroupindex
#105928212
C2×#635782
#105911302
C2×#635742
C3×#45542
#689843