Finite Group Databasebeta

← #11786660

Subgroups — #11786660

Order 1152.

583 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 583 conjugacy classes of subgroups — too many to draw. Only its 122 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#10594780C211yesmaximal, characteristic
2#10592809C211yesmaximal, characteristic
3#10591141C212yesmaximal, complemented
4#10591078C211yesmaximal, characteristic
5C3×#4552C212yesmaximal, complemented
6#68945—32nomaximal
7C2×#3828C2211yescharacteristic
8C22×C32×C8C2211yescharacteristic
9C2×#3748C2211yescharacteristic
10C2×C3×#208C2212yes—
11C2×C3×#208C2212yes—
12#63818—22no—
13#63817—24no—
14#63647—22no—
15#63577—24no—
16#63561C412yes—
17#63559C412yes—
18#5745—32no—
19#5132—32no—
20#5125—32no—
21#5124—32no—
22#5110—32no—
23#5110—61no—
24C3×#341—32no—
25#4552D312yescomplemented
26C22×C32×C4C2311yescharacteristic
27C2×#638Q812yes—
28#3828—22no—
29#3828—22no—
30C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
31C2×C4×C3⋊D3D412yes—
32C2×#634C2×C411yescharacteristic
33C2×C32×C8—21no—
34C2×C32×C8—22no—
35#3748—22no—
36C2×C3⋊(C3⋊C8)—21no—
37C3×#208—22no—
38C3×#208—22no—
39C3×#208C2×C414yes—
40C3×#208D414yes—
41C2×C3×C3⋊C8—22no—
42C2×C3×C3⋊C8—22no—
43#3712—24no—
44#3710—24no—
45#1858—91noSylow
46C2×#235—32no—
47C2×#235—61no—
48C2×C3×M16—32no—
49C2×C3×M16—32no—
50C22×C3×C8—21no—
51C22×C3×C8C2×D312yes—
52C2×#208—32no—
53C2×#208—61no—
54C2×#208C2×D312yes—
55C2×#208C2×D312yes—
56#907—64no—
57D3×M16—64no—
58#901—64no—
59#824—34no—
60#823—34no—
61#822—64no—
62(C2×D3)⋊C8—64no—
63(C2×D3)⋊C8—64no—
64#819—64no—
65C23×C32C2×Q811yescharacteristic
66C22×C3⋊D3C4⋊C412yes—
67C2×C32×C4C22×C411yescharacteristic
68C2×C32×C4C2×D412yes—
69C2×C32×C4C2×D411yescharacteristic
70C2×C32×C4#4112yes—
71#638—24no—
72C2×C3⋊Dic3C4⋊C412yes—
73C4⋊(C3⋊D3)—22no—
74C4×C3⋊D3—22no—
75C4×C3⋊D3—22no—
76#634—22no—
77C32×C8—41no—
78C3⋊(C3⋊C8)—41no—
79C3×C3⋊C8—24no—
80C3×C3⋊C8—24no—
81#568—91no—
82#430—92no—
83#413—91no—
84#408—91no—
85#341—32no—
86C22×C3×C4—21no—
87C22×C3×C4C22×D312yes—
88C2×#67—34no—
89C2×#67—62no—
90#235—62no—
91#235—62no—
92#235—62no—
93#235—62no—
94#235—122no—
95#235—122no—
96C2×D12—32no—
97C2×D12—61no—
98C2×C4×D3—34no—
99C2×C4×D3—62no—
100C2×Dic6—32no—
101C2×Dic6—61no—
102C3×M16—34no—
103C3×M16—34no—
104C3×M16—62no—
105C3×M16—62no—
106C2×C3×C8—22no—
107C2×C3×C8—22no—
108C2×C3×C8—22no—
109C2×C3×C8—22no—
110C2×C3×C8—42no—
111C2×C3×C8—62no—
112C2×C3×C8—62no—
113#208—22no—
114#208—22no—
115#208—62no—
116#208—62no—
117#208—122no—
118#208C4×D314yes—
119#208D1214yes—
120C2×C3⋊C8—22no—
121C2×C3⋊C8—22no—
122C2×C3⋊C8—62no—
123C2×C3⋊C8—62no—
124ΓL(1,𝔽25)—68no—
125D3×C8—68no—
126C22×C32—41no—
127C22×C32C2×C4⋊C411yescharacteristic
128C22×C32C22⋊Q812yes—
129C2×C3⋊D3—22no—
130C2×C3⋊D3—42no—
131C32×C4C4×D412yes—
132C32×C4#12011yescharacteristic
133C32×C4#12311yescharacteristic
134C3⋊Dic3—22no—
135C2×#41—91no—
136#131—184no—
137C2×M16—32no—
138C2×M16—32no—
139C2×M16—91no—
140C2×M16—182no—
141C22×C8D3211yescharacteristic
142#108—184no—
143#101—92no—
144#100—92no—
145C22⋊C8—182no—
146C23×C3—21no—
147C23×C3D3×Q812yes—
148C22×D3—34no—
149C22×D3—62no—
150C2×C3×C4—21no—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
153C2×C3×C4—21no—
154C2×C3×C4C2×C4×D312yes—
155C2×C3×C4C2×D1212yes—
156C2×C3×C4#23512yes—
157C2×C3×C4D3×D412yes—
158C2×C3×C4D3×D412yes—
159C2×C3×C4#23712yes—
160#67—64no—
161#67—64no—
162#67—124no—
163C2×Dic3—34no—
164C2×Dic3—62no—
165D12—62no—
166D12—62no—
167D12—122no—
168C4×D3—64no—
169C4×D3—64no—
170C4×D3—122no—
171C4×D3—122no—
172Dic6—62no—
173Dic6—62no—
174Dic6—122no—
175C3×C8—42no—
176C3×C8—42no—
177C3×C8—64no—
178C3×C8—64no—
179C3⋊C8—24no—
180C3⋊C8—24no—
181C3⋊C8—122no—
182C3⋊C8—122no—
183C2×C32—21no—
184C2×C32—22no—
185C2×C32#38511yescharacteristic
186C3⋊D3—42no—
187#41—182no—
188#41—182no—
189C2×Q8—91no—
190C2×D4—92no—
191C2×D4—91no—
192C22×C4—92no—
193C22×C4C2×D3211yescharacteristic
194M16—34no—
195M16—34no—
196M16—62no—
197M16—62no—
198M16—184no—
199M16—182no—
200C2×C8—22no—
201C2×C8—21no—
202C2×C8—62no—
203C2×C8—62no—
204C2×C8—184no—
205C2×C8—181no—
206C22×C3—21no—
207C22×C3—22no—
208C22×C3—42no—
209C22×C3—42no—
210C22×C3D3×C4⋊C412yes—
211C22×C3#89612yes—
212C22×C3#89712yes—
213C2×D3—64no—
214C2×D3—122no—
215C2×D3—124no—
216C2×D3—124no—
217C3×C4—22no—
218C3×C4—21no—
219C3×C4—21no—
220C3×C4C4×D1212yes—
221C3×C4#67⋊C412yes—
222C3×C4#88212yes—
223C3×C4#88312yes—
224Dic3—64no—
225Dic3—122no—
226C32#185811yescharacteristic, complemented, Sylow
227C23—92no—
228C23#379711yescharacteristic
229Q8—182no—
230D4—184no—
231D4—182no—
232C2×C4—92no—
233C2×C4—182no—
234C2×C4—182no—
235C2×C4C4×D3211yescharacteristic
236C2×C4D3×D1212yes—
237C2×C4#380412yes—
238C2×C4#381111yescharacteristic
239C8—41no—
240C8—64no—
241C8—64no—
242C8—361no—
243C2×C3—22no—
244C2×C3—22no—
245C2×C3—22no—
246C2×C3—22no—
247C2×C3—21no—
248C2×C3—42no—
249C2×C3#466812yes—
250D3—124no—
251D3—242no—
252C22—41no—
253C22—182no—
254C22—362no—
255C22#6388311yescharacteristic
256C22#6389512yes—
257C4—182no—
258C4#6388012yes—
259C4#6392311yescharacteristic
260C4#6397511yescharacteristic
261C3—21no—
262C3#6894512yescomplemented
263C2—21no—
264C2—22no—
265C2—362no—
266C2#1059137511yescharacteristic
subgroupG/H
centerC4#63923
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC2×C32#385
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1858
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. #10591141C2semidirect
5. C3×#4552C2semidirect
25. #4552D3semidirect
226. C32#1858semidirect
262. C3#68945semidirect

Maximal subgroups

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

subgroupindex
#105947802
#105928092
#105911412
#105910782
C3×#45522
#689453