Finite Group Databasebeta

← #11783837

Subgroups — #11783837

Order 1152.

550 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C2×#64116C211yesmaximal, characteristic
2#10593808C211yesmaximal, characteristic
3#10593792C211yesmaximal, characteristic
4#10593765C212yesmaximal, complemented
5#10590183C212yesmaximal, complemented
6C2×#3828C2211yescharacteristic
7#64286C2212yes—
8#64283C2212yes—
9C2×C32×M16C411yescharacteristic, complemented
10C22×C3⋊(C3⋊C8)C411yescharacteristic, complemented
11#64116—22no—
12#64116—22no—
13C2×#3743C411yescharacteristic, complemented
14C2×#3743C2211yescharacteristic
15C2×C8×C3⋊D3C411yescharacteristic, complemented
16C2×C8×C3⋊D3C2211yescharacteristic
17#63788C412yescomplemented
18#63786C412yes—
19#63780C412yescomplemented
20#63774C412yes—
21#63767—22no—
22C8×#157—22no—
23C2×#907—62no—
24C22×C32×C4C2×C411yescharacteristic
25C2×#638C2×C411yescharacteristic
26C2×#638C2×C411yescharacteristic
27#3828—22no—
28#3828—22no—
29C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
30C2×C4×C3⋊D3C2×C411yescharacteristic
31C2×C4×C3⋊D3C2311yescharacteristic
32C2×#634C2×C411yescharacteristic
33C22⋊#157C2×C414yes—
34#3792C2×C414yes—
35C4⋊#157—22no—
36C4×#157—22no—
37#3788—22no—
38#3787—22no—
39C32×M16—22no—
40C2×C32×C8C2×C411yescharacteristic
41C2×C32×C8C2×C411yescharacteristic
42C2×C3⋊(C3⋊C8)—21no—
43C2×C3⋊(C3⋊C8)—21no—
44C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
45C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
46#3743—22no—
47#3743—22no—
48C8×C3⋊D3—21no—
49C8×C3⋊D3—21no—
50C8×C3⋊D3D412yes—
51C8×C3⋊D3D412yes—
52#1757—91nomaximal, Sylow
53C2×#235—62no—
54C2×C3×M16—22no—
55C22×C3⋊C8—62no—
56#907—68no—
57#907—68no—
58C2×ΓL(1,𝔽25)—62no—
59C2×ΓL(1,𝔽25)—62no—
60C2×D3×C8—62no—
61C2×D3×C8—62no—
62C23×C32C4211yescharacteristic
63C22×C3⋊D3C4211yescharacteristic
64C22×C3⋊D3C22×C411yescharacteristic
65C2×#157—24no—
66C2×C32×C4—21no—
67C2×C32×C4—21no—
68C2×C32×C4C4211yescharacteristic
69C2×C32×C4C22×C411yescharacteristic
70#638—22no—
71#638—22no—
72C2×C3⋊Dic3C4211yescharacteristic
73C2×C3⋊Dic3C22×C411yescharacteristic
74C4⋊(C3⋊D3)—22no—
75C4×C3⋊D3—21no—
76C4×C3⋊D3—21no—
77C4×C3⋊D3C2×D412yes—
78C4×C3⋊D3#4112yes—
79#634—22no—
80#622—24no—
81C32×C8—21no—
82C32×C8C22⋊C412yes—
83C3⋊(C3⋊C8)—21no—
84C3⋊(C3⋊C8)C22⋊C411yescharacteristic
85C3⋊(C3⋊C8)C22⋊C411yescharacteristic
86C2×#131—91no—
87#413—91no—
88#410—91no—
89#405—92no—
90#344—92no—
91C22×C3×C4—22no—
92C2×#67—62no—
93C2×#67—62no—
94#235—68no—
95#235—68no—
96C2×D12—62no—
97C2×C4×D3—62no—
98C2×C4×D3—62no—
99C2×Dic6—62no—
100C3×M16—28no—
101C2×C3×C8—22no—
102C2×C3×C8—22no—
103C2×C3⋊C8—62no—
104C2×C3⋊C8—62no—
105C2×C3⋊C8—64no—
106C2×C3⋊C8—64no—
107ΓL(1,𝔽25)—68no—
108ΓL(1,𝔽25)—68no—
109D3×C8—64no—
110D3×C8—64no—
111D3×C8—64no—
112D3×C8—64no—
113C22×C32—21no—
114C22×C32—41no—
115C22×C32C2×C4211yescharacteristic
116C2×C3⋊D3—21no—
117C2×C3⋊D3—41no—
118C2×C3⋊D3—41no—
119C2×C3⋊D3C4×D412yes—
120#157—44no—
121C32×C4—21no—
122C32×C4C2×C22⋊C411yescharacteristic
123C32×C4#11711yescharacteristic
124C3⋊Dic3—21no—
125C3⋊Dic3C4×D412yes—
126C2×#41—91no—
127#131—182no—
128#131—182no—
129C2×M16—91no—
130C2×M16—91no—
131C2×M16—92no—
132C2×M16#15711yescharacteristic, complemented
133C22×C8—91no—
134C22×C8—91no—
135C22×C8—91no—
136#117—92no—
137#101—92no—
138#100—92no—
139#99—92no—
140#99—92no—
141#97—182no—
142C4×C8—182no—
143C23×C3—22no—
144C22×D3—62no—
145C22×D3—62no—
146C2×C3×C4—24no—
147C2×C3×C4—24no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150#67—68no—
151#67—68no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154D12—68no—
155C4×D3—64no—
156C4×D3—64no—
157C4×D3—64no—
158C4×D3—64no—
159Dic6—68no—
160C3×C8—24no—
161C3×C8—24no—
162C3⋊C8—62no—
163C3⋊C8—62no—
164C3⋊C8—64no—
165C2×C32—21no—
166C2×C32—41no—
167C2×C32C4×C22⋊C411yescharacteristic
168C3⋊D3—22no—
169C3⋊D3—41no—
170#41—182no—
171#41—182no—
172C2×Q8—91no—
173C2×D4—91no—
174C2×D4—91no—
175C2×D4—91no—
176C22×C4—91no—
177C22×C4—91no—
178C22×C4C2×#15711yescharacteristic
179M16—22no—
180M16—94no—
181M16—182no—
182M16—182no—
183M16—182no—
184C2×C8—91no—
185C2×C8—92no—
186C2×C8—92no—
187C2×C8—91no—
188C2×C8—181no—
189C2×C8—181no—
190C2×C8—181no—
191C2×C8—181no—
192C2×C8—182no—
193C2×C8C2×#15711yescharacteristic
194C2×C8C2×#15711yescharacteristic
195C4⋊C4—182no—
196C22⋊C4—94no—
197C42—182no—
198C22×C3—24no—
199C22×C3—22no—
200C22×C3—44no—
201C2×D3—64no—
202C2×D3—64no—
203C2×D3—124no—
204C2×D3—124no—
205C3×C4—24no—
206C3×C4—22no—
207C3×C4—22no—
208Dic3—64no—
209Dic3—64no—
210C32#175711yescharacteristic, complemented, Sylow
211C23—91no—
212C23—91no—
213C23C4×#15711yescharacteristic
214Q8—182no—
215D4—182no—
216D4—182no—
217D4—182no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—91no—
221C2×C4—92no—
222C2×C4—92no—
223C2×C4—91no—
224C2×C4—181no—
225C2×C4—181no—
226C2×C4—184no—
227C2×C4C4×#15711yescharacteristic
228C2×C4C22×#15711yescharacteristic
229C8—21no—
230C8—91no—
231C8—91no—
232C8—184no—
233C8—181no—
234C8C22⋊#15712yes—
235C2×C3—24no—
236C2×C3—22no—
237C2×C3—44no—
238D3—124no—
239D3—124no—
240C22—21no—
241C22—41no—
242C22—92no—
243C22—181no—
244C22—361no—
245C22—361no—
246C22C2×C4×#15711yescharacteristic
247C4—21no—
248C4—92no—
249C4—181no—
250C4—364no—
251C4#6428611yescharacteristic
252C4C2×C22⋊#15711yescharacteristic
253C3—22no—
254C2—21no—
255C2—41no—
256C2—182no—
257C2—361no—
258C2C4×C22⋊#15711yescharacteristic
subgroupG/H
centerC4C2×C22⋊#157
commutatorC22×C32C2×C42
FrattiniC2×C4C22×#157
FittingC2×C32×M16C4
socleC2×C32C4×C22⋊C4
prime radicalC2×#3828C22
cosocleC2×C4×C3⋊D3C23
hypercenterC2×M16#157
hypocenterC32#1757
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10593765C2semidirect
5. #10590183C2semidirect
9. C2×C32×M16C4semidirect
10. C22×C3⋊(C3⋊C8)C4semidirect
13. C2×#3743C4semidirect
15. C2×C8×C3⋊D3C4semidirect
17. #63788C4semidirect
19. #63780C4semidirect
132. C2×M16#157semidirect
210. C32#1757semidirect

Maximal subgroups

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

subgroupindex
C2×#641162
#105938082
#105937922
#105937652
#105901832
#17579