Finite Group Databasebeta

← #11790338

Subgroups — #11790338

Order 1152.

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

normal subgroups only

This group has 394 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×#63768C212yesmaximal
2#10593735C211yesmaximal, characteristic
3C4×C4⋊#157C211yesmaximal, characteristic
4C3⋊D3×C4⋊C8C211yesmaximal, characteristic
5#10590182C212yesmaximal
6C2×C4⋊#157—21no—
7C2×C4⋊#157—21no—
8C2×C4⋊#157C2212yes—
9C2×C4⋊#157C2211yescharacteristic
10C2×C4⋊#157C2211yescharacteristic
11C2×C4×#157—21no—
12C2×C8×C3⋊D3C2212yes—
13C42×C3⋊D3C2211yescharacteristic
14#63781—21no—
15#63768—24no—
16C32×C4⋊C8C411yescharacteristic, complemented
17#63641C412yescomplemented
18C4⋊(C3⋊(C3⋊C8))C411yescharacteristic, complemented
19D3×C4⋊C8—62no—
20C22×#157—21no—
21C22×#157—21no—
22C22×#157—22no—
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3C2311yescharacteristic
26C4⋊#157—22no—
27C4⋊#157—21no—
28C4⋊#157—21no—
29C4⋊#157—22no—
30C4⋊#157—42no—
31C4⋊#157—42no—
32C4⋊#157D412yes—
33C4⋊#157Q812yes—
34C4×#157—42no—
35C2×C32×C8C2×C412yes—
36C32×C42C2×C411yescharacteristic
37C4×C3⋊Dic3C2×C411yescharacteristic
38C4×C3⋊Dic3Q811yescharacteristic
39C4×C3⋊Dic3Q811yescharacteristic
40C2×C3⋊(C3⋊C8)C2×C412yes—
41C8×C3⋊D3—22no—
42C8×C3⋊D3—22no—
43#1948—91nomaximal, Sylow
44C2×D3×C8—64no—
45C42×D3—62no—
46C3×C4⋊C8—22no—
47Dic3⋊C8—64no—
48C4⋊(C3⋊C8)—62no—
49C22×C3⋊D3C2×D411yescharacteristic
50C2×#157—22no—
51C2×#157—22no—
52C2×#157—41no—
53C2×#157—41no—
54C2×#157—41no—
55C2×#157—41no—
56C2×#157—42no—
57C2×#157—42no—
58C2×#157—42no—
59C2×C32×C4C4⋊C411yescharacteristic
60C2×C32×C4C4⋊C411yescharacteristic
61C2×C32×C4C22×C411yescharacteristic
62C2×C3⋊Dic3C4⋊C411yescharacteristic
63C2×C3⋊Dic3C4⋊C411yescharacteristic
64C2×C3⋊Dic3C2×Q811yescharacteristic
65C4×C3⋊D3—21no—
66C4×C3⋊D3—21no—
67C4×C3⋊D3SD1612yes—
68C4×C3⋊D3SD1612yes—
69C4×C3⋊D3C2×D411yescharacteristic
70C4×C3⋊D3C2×Q811yescharacteristic
71C4×C3⋊D3#4111yescharacteristic
72C4×C3⋊D3#4111yescharacteristic
73C32×C8—22no—
74C3⋊(C3⋊C8)—22no—
75C2×#106—92no—
76C2×C4⋊C8—91no—
77#384—91no—
78C4×C4⋊C4—91no—
79#340—92no—
80C2×C4×D3—62no—
81C2×C4×D3—62no—
82C2×C4×D3—62no—
83C2×C3×C8—24no—
84C3×C42—22no—
85C4×Dic3—62no—
86C4×Dic3—62no—
87C4×Dic3—62no—
88C2×C3⋊C8—64no—
89D3×C8—124no—
90D3×C8—124no—
91C22×C32C2×C4⋊C411yescharacteristic
92C2×C3⋊D3#12111yescharacteristic
93C2×C3⋊D3C22⋊Q811yescharacteristic
94C2×C3⋊D3C2×SD1611yescharacteristic
95C2×C3⋊D3C2×SD1611yescharacteristic
96C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
97C2×C3⋊D3#13711yescharacteristic
98#157—42no—
99#157—42no—
100#157—82no—
101C32×C4—21no—
102C32×C4#10612yescomplemented
103C32×C4C4×D411yescharacteristic
104C32×C4C4×Q811yescharacteristic
105C3⋊Dic3—21no—
106C3⋊Dic3#10612yescomplemented
107C3⋊Dic3#12511yescharacteristic
108C3⋊Dic3C4⋊Q811yescharacteristic
109C22×C8—92no—
110C2×C4⋊C4—91no—
111C2×C4⋊C4—91no—
112C2×C4⋊C4—92no—
113C2×C4⋊C4—181no—
114C2×C4⋊C4—181no—
115C2×C42—91no—
116C2×C42—181no—
117#106—184no—
118C4⋊C8—92no—
119C4⋊C8—91no—
120C4⋊C8#15711yescharacteristic, complemented
121#95—181no—
122C22×D3—62no—
123C2×C3×C4—22no—
124C2×C3×C4—22no—
125C2×C3×C4—22no—
126C2×Dic3—62no—
127C2×Dic3—62no—
128C2×Dic3—62no—
129C4×D3—64no—
130C4×D3—64no—
131C4×D3—62no—
132C4×D3—62no—
133C4×D3—62no—
134C4×D3—62no—
135C4×D3—122no—
136C4×D3—122no—
137C3×C8—44no—
138C3⋊C8—124no—
139C2×C32#38911yescharacteristic
140C2×C32C2×#10611yescharacteristic
141C2×C32#42811yescharacteristic
142C3⋊D3#46011yescharacteristic
143C3⋊D3#46111yescharacteristic
144C3⋊D3#47511yescharacteristic
145C3⋊D3#47611yescharacteristic
146C22×C4—91no—
147C22×C4—91no—
148C22×C4—91no—
149C22×C4—181no—
150C22×C4—181no—
151C22×C4—182no—
152C2×C8—92no—
153C2×C8—182no—
154C2×C8—182no—
155C2×C8C2×#15712yes—
156C4⋊C4—92no—
157C4⋊C4—92no—
158C4⋊C4—181no—
159C4⋊C4—181no—
160C4⋊C4—182no—
161C4⋊C4—182no—
162C4⋊C4—362no—
163C4⋊C4—362no—
164C42—91no—
165C42—91no—
166C42—91no—
167C42—362no—
168C42C2×#15711yescharacteristic
169C22×C3—22no—
170C2×D3—62no—
171C2×D3—62no—
172C2×D3—62no—
173C2×D3—62no—
174C2×D3—62no—
175C2×D3—62no—
176C3×C4—24no—
177C3×C4—22no—
178C3×C4—22no—
179C3×C4—42no—
180Dic3—64no—
181Dic3—62no—
182Dic3—62no—
183Dic3—122no—
184C32#194811yescharacteristic, complemented, Sylow
185C23—91no—
186C2×C4—91no—
187C2×C4—91no—
188C2×C4—92no—
189C2×C4—92no—
190C2×C4—91no—
191C2×C4—91no—
192C2×C4—91no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—181no—
196C2×C4—181no—
197C2×C4—182no—
198C2×C4—182no—
199C2×C4—361no—
200C2×C4—361no—
201C2×C4—361no—
202C2×C4—361no—
203C2×C4—362no—
204C2×C4—362no—
205C2×C4—362no—
206C2×C4C4⋊#15711yescharacteristic
207C2×C4C4⋊#15711yescharacteristic
208C2×C4C22×#15711yescharacteristic
209C8—22no—
210C8—182no—
211C2×C3—22no—
212C2×C3—22no—
213C2×C3—22no—
214D3—62no—
215D3—62no—
216D3—62no—
217D3—62no—
218C22—91no—
219C22—91no—
220C22—91no—
221C22—91no—
222C22—91no—
223C22—91no—
224C22C2×C4⋊#15711yescharacteristic
225C4—21no—
226C4—91no—
227C4—91no—
228C4—92no—
229C4—181no—
230C4—362no—
231C4—362no—
232C4—722no—
233C4#6376812yescomplemented
234C4D4×#15711yescharacteristic
235C4Q8×#15711yescharacteristic
236C3—22no—
237C2—91no—
238C2—91no—
239C2—91no—
240C2—91no—
241C2#1059375911yescharacteristic
242C2C2×#6376811yescharacteristic
243C2#1059377411yescharacteristic
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4⋊C8C4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊C8#157
hypocenterC32#1948
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
16. C32×C4⋊C8C4semidirect
17. #63641C4semidirect
18. C4⋊(C3⋊(C3⋊C8))C4semidirect
102. C32×C4#106semidirect
106. C3⋊Dic3#106semidirect
120. C4⋊C8#157semidirect
184. C32#1948semidirect
233. C4#63768semidirect

Maximal subgroups

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

subgroupindex
C2×#637682
#105937352
C4×C4⋊#1572
C3⋊D3×C4⋊C82
#105901822
#19489