Finite Group Databasebeta

← #11878878

Subgroups — #11878878

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 279 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#533C211yesmaximal, characteristic
2C2×#64078C211yesmaximal, characteristic
3#10592792C212yesmaximal, complemented
4#10592791C212yesmaximal, complemented
5#10592749C214yesmaximal
6#10592730C214yesmaximal, complemented
7#10592624C211yesmaximal, characteristic
8#83370—34nomaximal
9C22×#634C2212yes—
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4⋊Q8C2211yescharacteristic
12C32×#125—21no—
13C32×C22⋊Q8—21no—
14C32×C22⋊Q8C2212yes—
15C32×C4×Q8—21no—
16C32×C4×Q8C2212yes—
17C32×#117—21no—
18C2×C32×C42C2211yescharacteristic
19C2×#3756C2218yes—
20C2×C4⋊(C3⋊Dic3)—21no—
21C2×C4⋊(C3⋊Dic3)—21no—
22#64078—21no—
23#64078—21no—
24#64078C2212yes—
25#64078C2212yes—
26#63657C2212yes—
27#63637C2218yes—
28C4⋊(C3⋊(C3⋊C8))C2212yes—
29C4×C3⋊(C3⋊C8)C2212yes—
30C3×#533D314yes—
31C2×#869—34no—
32#5093—38no—
33#5092—38no—
34#5050—316no—
35#5031—316no—
36#4925—34no—
37C2×C32×Q8—21no—
38C2×C32×Q8C2312yes—
39C22×C32×C4D411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3—22no—
43C2×#634—22no—
44C2×#634—44no—
45C2×#634C2314yes—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—22no—
50C32×C4⋊C4—22no—
51C32×C4⋊C4C2312yes—
52C32×C22⋊C4—22no—
53C32×C42—22no—
54C32×C42D411yescharacteristic
55C32×C42D411yescharacteristic
56C32×C42C2311yescharacteristic
57C32×C42C2311yescharacteristic
58#3756—48no—
59C4⋊(C3⋊Dic3)—22no—
60C4⋊(C3⋊Dic3)—22no—
61C4⋊(C3⋊Dic3)—22no—
62C4⋊(C3⋊Dic3)—22no—
63C2×C3⋊(C3⋊C8)C2314yes—
64#3209—91noSylow
65C22×Dic6—38no—
66C3×C4⋊Q8C2×D314yes—
67C3×C4⋊Q8C2×D314yes—
68C3×#125—24no—
69C3×C22⋊Q8—24no—
70C3×C22⋊Q8C2×D318yes—
71C3×C4×Q8—24no—
72C3×C4×Q8C2×D318yes—
73C3×#117—24no—
74C2×C3×C42C2×D314yes—
75C2×#216—332no—
76C2×C4⋊Dic3—64no—
77C2×C4⋊Dic3—64no—
78#869—38no—
79#869—38no—
80#869—64no—
81#869—64no—
82#830—38no—
83#810—332no—
84C4⋊(C3⋊C8)—38no—
85C4×C3⋊C8—38no—
86C23×C32C2×D411yescharacteristic
87C32×Q8—24no—
88C32×Q8—42no—
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4—22no—
92C2×C32×C4—22no—
93C2×C32×C4Q1614yescomplemented
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2411yescharacteristic
100C2×C3⋊Dic3—24no—
101C2×C3⋊Dic3—44no—
102#634—28no—
103#634—44no—
104C3⋊(C3⋊C8)—24no—
105#533C3⋊D311yescharacteristic
106C2×C4⋊Q8—91no—
107#494—92no—
108#487—92no—
109#462—94no—
110#451—94no—
111#431—91no—
112C2×C3×Q8—24no—
113C2×C3×Q8C22×D318yes—
114C22×C3×C4#6714yes—
115C22×C3×C4#6714yes—
116C22×C3×C4C22×D314yes—
117C22×Dic3—68no—
118C2×Dic6—316no—
119C2×Dic6—68no—
120C2×Dic6—1216no—
121C3×C4⋊C4—24no—
122C3×C4⋊C4—24no—
123C3×C4⋊C4—24no—
124C3×C4⋊C4—28no—
125C3×C4⋊C4—28no—
126C3×C4⋊C4C22×D318yes—
127C3×C22⋊C4—28no—
128C3×C42—28no—
129C3×C42#6714yes—
130C3×C42#6714yes—
131C3×C42C22×D314yes—
132C3×C42C22×D314yes—
133#216—1232no—
134C4⋊Dic3—68no—
135C4⋊Dic3—68no—
136C4⋊Dic3—68no—
137C4⋊Dic3—68no—
138C2×C3⋊C8—316no—
139C22×C32—21no—
140C22×C32—21no—
141C22×C32C2×Q1612yes—
142C22×C32C22×D411yescharacteristic
143C32×C4—21no—
144C32×C4—21no—
145C32×C4—42no—
146C32×C4—42no—
147C32×C4C2×Q1612yes—
148C32×C4C2×Q1612yes—
149C32×C4#13712yes—
150C32×C4H(5,𝔽2)12yes—
151C3⋊Dic3—44no—
152C22×Q8—92no—
153C2×Q16—98no—
154C4⋊Q8—92no—
155C4⋊Q8—92no—
156C4⋊Q8—181no—
157C4⋊Q8—181no—
158C4⋊Q8C2×C3⋊D311yescharacteristic
159C4⋊Q8C2×C3⋊D311yescharacteristic
160#125—21no—
161C22⋊Q8—21no—
162C22⋊Q8C2×C3⋊D312yes—
163C4×Q8—21no—
164C4×Q8C2×C3⋊D312yes—
165#117—21no—
166C2×C4⋊C4—181no—
167C2×C4⋊C4—181no—
168C2×C42C2×C3⋊D311yescharacteristic
169C4⋊C8—92no—
170#103—98no—
171C22⋊C8—92no—
172C4×C8—92no—
173C23×C3C2×#6714yes—
174C3×Q8—216no—
175C3×Q8—48no—
176C2×C3×C4—28no—
177C2×C3×C4—28no—
178C2×C3×C4—28no—
179C2×C3×C4—28no—
180C2×C3×C4#216116yescomplemented
181C2×C3×C4C2×#6714yes—
182C2×C3×C4C2×#6714yes—
183C2×C3×C4C2×#6714yes—
184C2×C3×C4C2×#6714yes—
185C2×C3×C4C2×#6714yes—
186C2×C3×C4C23×D314yes—
187C2×Dic3—616no—
188C2×Dic3—1216no—
189Dic6—632no—
190Dic6—1216no—
191C3⋊C8—616no—
192C2×C32—22no—
193C2×C32#53511yescharacteristic
194C2×C32C22×Q1611yescharacteristic
195C2×C32C2×#13711yescharacteristic
196C2×Q8—21no—
197C2×Q8—94no—
198C2×Q8—182no—
199C2×Q8—364no—
200C2×Q8C22×C3⋊D312yes—
201C22×C4—182no—
202C22×C4#63811yescharacteristic
203C22×C4#63811yescharacteristic
204C22×C4C22×C3⋊D311yescharacteristic
205Q16—368no—
206C2×C8—94no—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—182no—
213C4⋊C4—182no—
214C4⋊C4—182no—
215C4⋊C4—182no—
216C4⋊C4C22×C3⋊D312yes—
217C22⋊C4—22no—
218C42—22no—
219C42#63811yescharacteristic
220C42#63811yescharacteristic
221C42C22×C3⋊D311yescharacteristic
222C42C22×C3⋊D311yescharacteristic
223C22×C3—24no—
224C22×C3—24no—
225C22×C3C2×#21618yes—
226C22×C3C22×#6714yes—
227C3×C4—24no—
228C3×C4—24no—
229C3×C4—48no—
230C3×C4—48no—
231C3×C4C2×#21618yes—
232C3×C4C2×#21618yes—
233C3×C4#95118yes—
234C3×C4#100918yes—
235Dic3—1216no—
236C32#320911yescharacteristic, complemented, Sylow
237C23C2×#63811yescharacteristic
238Q8—24no—
239Q8—42no—
240Q8—188no—
241Q8—364no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—184no—
247C2×C4—364no—
248C2×C4#375614yescomplemented
249C2×C4C2×#63811yescharacteristic
250C2×C4C2×#63811yescharacteristic
251C2×C4C2×#63811yescharacteristic
252C2×C4C2×#63811yescharacteristic
253C2×C4C2×#63811yescharacteristic
254C2×C4C23×C3⋊D311yescharacteristic
255C8—184no—
256C2×C3—28no—
257C2×C3C22×#21614yes—
258C2×C3C2×#95114yes—
259C2×C3#583014yes—
260C22—21no—
261C22—21no—
262C22C2×#375612yes—
263C22C22×#63811yescharacteristic
264C4—21no—
265C4—21no—
266C4—42no—
267C4—42no—
268C4—364no—
269C4C2×#375612yes—
270C4C2×#375612yes—
271C4#6416012yes—
272C4#6436612yes—
273C3#8337014yescomplemented
274C2—22no—
275C2C22×#375611yescharacteristic
276C2C2×#6416011yescharacteristic
277C2#1059630111yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#533C2
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenter#533C3⋊D3
hypocenterC32#3209
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #10592792C2semidirect
4. #10592791C2semidirect
6. #10592730C2semidirect
93. C2×C32×C4Q16semidirect
180. C2×C3×C4#216semidirect
236. C32#3209semidirect
248. C2×C4#3756semidirect
273. C3#83370semidirect

Maximal subgroups

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

subgroupindex
C32×#5332
C2×#640782
#105927922
#105927912
#105927492
#105927302
#105926242
#833703