Finite Group Databasebeta

← #11785435

Subgroups — #11785435

Order 1152.

630 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C22×C8×C3⋊D3C211yesmaximal, characteristic
2#10593803C212yesmaximal
3C2×#63770C212yesmaximal, complemented
4#10590185C212yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3788C2214yes—
7C22×C32×C8C411yescharacteristic
8C22×C3⋊(C3⋊C8)C411yescharacteristic
9C2×C8×C3⋊D3—24no—
10C2×C8×C3⋊D3C411yescharacteristic
11C2×C8×C3⋊D3C411yescharacteristic
12C2×C8×C3⋊D3C2211yescharacteristic
13C2×C8×C3⋊D3C2211yescharacteristic
14C22⋊#622—22no—
15#63778—22no—
16#63770—24no—
17C22×D3×C8—62no—
18C23×C3⋊D3Q811yescharacteristic
19C22×C32×C4C2×C411yescharacteristic
20C22×C3⋊Dic3D411yescharacteristic
21C2×C4×C3⋊D3—22no—
22C2×C4×C3⋊D3—22no—
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3Q811yescharacteristic
26C2×C4×C3⋊D3C2311yescharacteristic
27C2×#622—24no—
28#3788—24no—
29#3788—24no—
30C2×C32×C8—22no—
31C2×C32×C8C2×C411yescharacteristic
32C2×C32×C8C2×C411yescharacteristic
33C2×C3⋊(C3⋊C8)—22no—
34C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
35C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
36C8×C3⋊D3—22no—
37C8×C3⋊D3—22no—
38C8×C3⋊D3—22no—
39C8×C3⋊D3D414yes—
40#1810—91nomaximal, Sylow
41C22×C4×D3—62no—
42C22×C3×C8—22no—
43C22×C3⋊C8—62no—
44C2×D3×C8—62no—
45C2×D3×C8—62no—
46C2×D3×C8—62no—
47C2×D3×C8—62no—
48C2×D3×C8—616no—
49C23×C32C4⋊C411yescharacteristic
50C22×C3⋊D3—22no—
51C22×C3⋊D3—22no—
52C22×C3⋊D3—22no—
53C22×C3⋊D3C4⋊C411yescharacteristic
54C22×C3⋊D3C2×Q811yescharacteristic
55C2×C32×C4—21no—
56C2×C32×C4—21no—
57C2×C32×C4C4⋊C411yescharacteristic
58C2×C32×C4C22×C411yescharacteristic
59C2×C3⋊Dic3—22no—
60C2×C3⋊Dic3C4⋊C411yescharacteristic
61C2×C3⋊Dic3C2×D411yescharacteristic
62C4×C3⋊D3—22no—
63C4×C3⋊D3—21no—
64C4×C3⋊D3—21no—
65C4×C3⋊D3—22no—
66C4×C3⋊D3C2×D412yes—
67C4×C3⋊D3#4112yes—
68#622—44no—
69C32×C8—21no—
70C32×C8C22⋊C412yes—
71C3⋊(C3⋊C8)—21no—
72C3⋊(C3⋊C8)C22⋊C412yes—
73C23×C8—91no—
74C2×#108—92no—
75#407—92no—
76#341—92no—
77C23×D3—62no—
78C22×C3×C4—22no—
79C22×Dic3—62no—
80C2×C4×D3—62no—
81C2×C4×D3—62no—
82C2×C4×D3—62no—
83C2×C4×D3—62no—
84C2×C4×D3—68no—
85C2×C4×D3—68no—
86C2×C3×C8—28no—
87C2×C3×C8—22no—
88C2×C3×C8—22no—
89C2×C3⋊C8—62no—
90C2×C3⋊C8—62no—
91C2×C3⋊C8—68no—
92D3×C8—68no—
93D3×C8—68no—
94D3×C8—68no—
95D3×C8—68no—
96C22×C32—21no—
97C22×C32—21no—
98C22×C32#10812yescomplemented
99C22×C32C2×C4⋊C411yescharacteristic
100C2×C3⋊D3—28no—
101C2×C3⋊D3—21no—
102C2×C3⋊D3—21no—
103C2×C3⋊D3—21no—
104C2×C3⋊D3—21no—
105C2×C3⋊D3#10812yescomplemented
106C2×C3⋊D3C22⋊Q812yes—
107C32×C4—21no—
108C32×C4C2×C22⋊C411yescharacteristic
109C32×C4#11711yescharacteristic
110C3⋊Dic3—21no—
111C3⋊Dic3#12112yes—
112C23×C4—91no—
113C2×M16—94no—
114C22×C8—91no—
115C22×C8—91no—
116C22×C8—91no—
117C22×C8—91no—
118C22×C8—91no—
119C22×C8—184no—
120C22×C8#15711yescharacteristic
121#108—184no—
122C22⋊C8—182no—
123C22⋊C8—182no—
124C23×C3—22no—
125C22×D3—62no—
126C22×D3—62no—
127C22×D3—68no—
128C22×D3—68no—
129C22×D3—68no—
130C2×C3×C4—24no—
131C2×C3×C4—24no—
132C2×C3×C4—22no—
133C2×C3×C4—22no—
134C2×Dic3—62no—
135C2×Dic3—62no—
136C2×Dic3—68no—
137C4×D3—64no—
138C4×D3—64no—
139C4×D3—64no—
140C4×D3—68no—
141C4×D3—68no—
142C4×D3—64no—
143C3×C8—24no—
144C3×C8—24no—
145C3⋊C8—64no—
146C3⋊C8—64no—
147C2×C32—22no—
148C2×C32#38011yescharacteristic
149C2×C32C2×#10811yescharacteristic
150C2×C32C2×#10811yescharacteristic
151C3⋊D3—22no—
152C3⋊D3—22no—
153C24—91no—
154C22×C4—91no—
155C22×C4—91no—
156C22×C4—91no—
157C22×C4—91no—
158C22×C4—91no—
159C22×C4—182no—
160C22×C4—182no—
161C22×C4C2×#15711yescharacteristic
162M16—184no—
163M16—184no—
164C2×C8—22no—
165C2×C8—91no—
166C2×C8—94no—
167C2×C8—91no—
168C2×C8—182no—
169C2×C8—182no—
170C2×C8—182no—
171C2×C8—182no—
172C2×C8—184no—
173C2×C8C2×#15711yescharacteristic
174C2×C8C2×#15711yescharacteristic
175C22×C3—24no—
176C22×C3—24no—
177C22×C3—24no—
178C22×C3—22no—
179C2×D3—64no—
180C2×D3—64no—
181C2×D3—64no—
182C2×D3—632no—
183C2×D3—64no—
184C2×D3—64no—
185C2×D3—64no—
186C3×C4—24no—
187C3×C4—22no—
188C3×C4—22no—
189Dic3—64no—
190Dic3—64no—
191C32#181011yescharacteristic, complemented, Sylow
192C23—91no—
193C23—91no—
194C23—182no—
195C23—182no—
196C23—182no—
197C23C4⋊#15711yescharacteristic
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—91no—
201C2×C4—92no—
202C2×C4—92no—
203C2×C4—91no—
204C2×C4—182no—
205C2×C4—182no—
206C2×C4—182no—
207C2×C4—181no—
208C2×C4—181no—
209C2×C4C4⋊#15711yescharacteristic
210C2×C4C22×#15711yescharacteristic
211C8—21no—
212C8—92no—
213C8—181no—
214C8—364no—
215C8C22⋊#15712yes—
216C2×C3—28no—
217C2×C3—22no—
218C2×C3—22no—
219C2×C3—22no—
220D3—68no—
221D3—68no—
222C22—21no—
223C22—21no—
224C22—92no—
225C22—92no—
226C22—188no—
227C22—181no—
228C22—181no—
229C22—181no—
230C22—181no—
231C22#6377012yescomplemented
232C22C2×C4⋊#15711yescharacteristic
233C4—21no—
234C4—92no—
235C4—181no—
236C4#6428611yescharacteristic
237C4C2×C22⋊#15711yescharacteristic
238C3—22no—
239C2—22no—
240C2—182no—
241C2—182no—
242C2C2×#6377011yescharacteristic
243C2#1059377111yescharacteristic
244C2#1059381211yescharacteristic
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC22×C32×C8C4
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3Q8
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C8#157
hypocenterC32#1810
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×#63770C2semidirect
4. #10590185C2semidirect
98. C22×C32#108semidirect
105. C2×C3⋊D3#108semidirect
191. C32#1810semidirect
231. C22#63770semidirect

Maximal subgroups

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

subgroupindex
C22×C8×C3⋊D32
#105938032
C2×#637702
#105901852
#18109