Finite Group Databasebeta

← #11796854

Subgroups — #11796854

Order 1152.

490 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 62 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×#64121C211yesmaximal, characteristic
2#10593768C211yesmaximal, characteristic, complemented
3#10593762C211yesmaximal, characteristic, complemented
4#10590192C214yesmaximal, complemented
5C2×#3830—21no—
6#64286—21no—
7C2×C32×D8C411yescharacteristic, complemented
8C2×#3754—21no—
9#64121—21no—
10#64121—21no—
11#64121C412yescomplemented
12#64121C2212yes—
13C2×#3746C411yescharacteristic, complemented
14C2×C8×C3⋊D3C2211yescharacteristic
15#63773—21no—
16#63769—21no—
17#63768C2212yescomplemented
18#63765C2212yescomplemented
19#63764—21no—
20C2×#912—62no—
21C2×C32×D4—21no—
22C2×#638—41no—
23C22×C3⋊Dic3—41no—
24#3830—22no—
25#3830—22no—
26#3830—41no—
27#3830—41no—
28C2×C4×C3⋊D3D411yescharacteristic
29C2×#634—21no—
30C22⋊#157—41no—
31C4⋊#157—22no—
32C4×#157—41no—
33C32×D8—21no—
34C32×D8C2×C412yes—
35C2×C32×C8C2×C411yescharacteristic
36#3754—22no—
37#3754—22no—
38C2×C3⋊(C3⋊C8)D411yescharacteristic
39#3746—21no—
40#3746C2×C412yes—
41C8×C3⋊D3C2×C411yescharacteristic
42C8×C3⋊D3D411yescharacteristic
43C8×C3⋊D3D411yescharacteristic
44C8×C3⋊D3C2311yescharacteristic
45#3708—22no—
46#2145—91nomaximal, Sylow
47C2×#237—64no—
48C2×C3×D8—22no—
49C2×#214—64no—
50#912—64no—
51#912—64no—
52#912—64no—
53#912—64no—
54C2×Dic12—62no—
55C2×D3×C8—62no—
56C23×C32—41no—
57C22×C3⋊D3D811yescharacteristic
58C2×#157—42no—
59C32×D4—22no—
60C32×D4—41no—
61C2×C32×C4C22⋊C411yescharacteristic
62#638—42no—
63#638—42no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3—42no—
66C2×C3⋊Dic3—42no—
67C2×C3⋊Dic3SD1611yescharacteristic
68C4×C3⋊D3C22⋊C411yescharacteristic
69C4×C3⋊D3D811yescharacteristic
70C4×C3⋊D3SD1611yescharacteristic
71C4×C3⋊D3C2×D411yescharacteristic
72#634—22no—
73#634—41no—
74C32×C8C22⋊C411yescharacteristic
75C32×C8C22×C411yescharacteristic
76C3⋊(C3⋊C8)C22⋊C411yescharacteristic
77C3⋊(C3⋊C8)C2×D411yescharacteristic
78C2×#135—91no—
79C2×M32—91no—
80#427—91no—
81#360—94no—
82C2×C3×D4—24no—
83C2×#67—124no—
84C22×Dic3—124no—
85#237—68no—
86#237—68no—
87#237—124no—
88#237—124no—
89C2×C4×D3—62no—
90C2×Dic6—64no—
91C3×D8—24no—
92C3×D8—24no—
93C2×C3×C8—22no—
94#214—68no—
95#214—68no—
96C2×C3⋊C8—62no—
97Dic12—64no—
98Dic12—64no—
99D3×C8—62no—
100D3×C8—62no—
101D3×C8—62no—
102D3×C8—62no—
103C22×C32—42no—
104C22×C32—82no—
105C22×C32#10211yescharacteristic
106C2×C3⋊D3—41no—
107C2×C3⋊D3#10211yescharacteristic
108C2×C3⋊D3C2×D811yescharacteristic
109#157—82no—
110C32×C4#10211yescharacteristic
111C32×C4C2×C22⋊C411yescharacteristic
112C3⋊Dic3—42no—
113C3⋊Dic3#10211yescharacteristic
114C3⋊Dic3C2×SD1611yescharacteristic
115C2×#41—181no—
116#135—92no—
117#135—92no—
118#135—181no—
119#135—181no—
120C2×Q16—91no—
121C2×SD16—181no—
122C2×D8#15711yescharacteristic, complemented
123C22×C8—91no—
124#117—181no—
125M32—92no—
126M32—181no—
127C2×C16—181no—
128#107—181no—
129#106—92no—
130C23×C3—44no—
131C22×D3—62no—
132C3×D4—28no—
133C3×D4—44no—
134C2×C3×C4—22no—
135#67—128no—
136#67—128no—
137C2×Dic3—62no—
138C2×Dic3—128no—
139C2×Dic3—128no—
140C2×Dic3—124no—
141C4×D3—62no—
142C4×D3—62no—
143C4×D3—62no—
144C4×D3—62no—
145Dic6—68no—
146Dic6—124no—
147C3×C8—22no—
148C3×C8—22no—
149C3⋊C8—62no—
150C3⋊C8—62no—
151C2×C32—21no—
152C2×C32—82no—
153C2×C32C2×#10211yescharacteristic
154C3⋊D3—21no—
155C3⋊D3—21no—
156#41—182no—
157#41—182no—
158#41—361no—
159#41—361no—
160C2×Q8—181no—
161C2×D4—21no—
162C2×D4—361no—
163C22×C4—91no—
164C22×C4—361no—
165Q16—92no—
166Q16—181no—
167SD16—182no—
168SD16—182no—
169D8—21no—
170D8C2×#15712yes—
171C2×C8—91no—
172C2×C8—91no—
173C2×C8—91no—
174C2×C8—91no—
175C2×C8—91no—
176C2×C8C2×#15711yescharacteristic
177C4⋊C4—182no—
178C22⋊C4—361no—
179C42—361no—
180C16—182no—
181C22×C3—22no—
182C22×C3—48no—
183C22×C3—88no—
184C2×D3—62no—
185C2×D3—62no—
186C2×D3—124no—
187C3×C4—22no—
188C3×C4—22no—
189Dic3—62no—
190Dic3—62no—
191Dic3—128no—
192C32#214511yescharacteristic, complemented, Sylow
193C23—41no—
194C23—91no—
195Q8—182no—
196Q8—361no—
197D4—22no—
198D4—41no—
199D4—362no—
200D4—362no—
201C2×C4—91no—
202C2×C4—91no—
203C2×C4—91no—
204C2×C4—91no—
205C2×C4—91no—
206C2×C4—362no—
207C2×C4—362no—
208C2×C4—361no—
209C2×C4—362no—
210C2×C4C22⋊#15711yescharacteristic
211C8—91no—
212C8—91no—
213C8C22⋊#15711yescharacteristic
214C8C22×#15711yescharacteristic
215C2×C3—24no—
216C2×C3—22no—
217C2×C3—88no—
218D3—122no—
219D3—122no—
220C22—42no—
221C22—82no—
222C22—91no—
223C22—91no—
224C22—361no—
225C22#6378211yescharacteristic
226C4—91no—
227C4—91no—
228C4—362no—
229C4—722no—
230C4#6378211yescharacteristic
231C4C2×C22⋊#15711yescharacteristic
232C3—22no—
233C2—21no—
234C2—82no—
235C2—181no—
236C2—181no—
237C2C2×#6378211yescharacteristic
subgroupG/H
centerC2C2×#63782
commutatorC32×C8C22×C4
FrattiniC8C22×#157
FittingC2×C32×D8C4
socleC2×C32C2×#102
prime radicalC2×#64121C2
cosocleC8×C3⋊D3C23
hypercenterC2×D8#157
hypocenterC32#2145
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #10593768C2semidirect
3. #10593762C2semidirect
4. #10590192C2semidirect
7. C2×C32×D8C4semidirect
11. #64121C4semidirect
13. C2×#3746C4semidirect
17. #63768C22semidirect
18. #63765C22semidirect
122. C2×D8#157semidirect
192. C32#2145semidirect

Maximal subgroups

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

subgroupindex
C2×#641212
#105937682
#105937622
#105901922
#21459