Finite Group Databasebeta

← #11803828

Subgroups — #11803828

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 303 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64078C211yesmaximal, characteristic
2C2×#63844C212yesmaximal
3C3×#4936C211yesmaximal, characteristic
4C3×#4932C211yesmaximal, characteristic
5#10591271C218yesmaximal
6#10591213C212yesmaximal
7#74152—31nomaximal
8#73388—31nomaximal
9C22×#634C2212yes—
10C2×C32×C42C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2214yes—
12#64078C418yescomplemented
13C2×C3×C4⋊Dic3C2212yes—
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×#3724C2214yes—
17C2×Dic32C2214yes—
18#63844—28no—
19C3×C3⋊#95C2214yes—
20C3×C3⋊#95C2214yes—
21#63579C2218yes—
22C2×#887—32no—
23C2×#869—31no—
24C2×#869—31no—
25C2×#869—61no—
26C2×C4×Dic6—32no—
27C3×#382—31no—
28C3×#376—31no—
29#4973—32no—
30#4936D311yescharacteristic
31#4932D311yescharacteristic
32#4929—32no—
33#4654—38no—
34#4653—38no—
35C22×C32×C4C2312yes—
36C22×C32×C4C2311yescharacteristic
37C22×C3⋊Dic3C2314yes—
38C2×#634—24no—
39C2×#634—24no—
40C2×#634C2×C418yes—
41C22×C3×Dic3C2312yes—
42C22×C3×Dic3C2314yes—
43C22×C3×Dic3C2312yes—
44C32×C42C2×C414yes—
45C4⋊(C3⋊Dic3)C2×C4116yes—
46C3×C4⋊Dic3—24no—
47C3×C4×Dic3—22no—
48C3×C4×Dic3D414yes—
49#3724—28no—
50Dic32—28no—
51#2327—91noSylow
52C22×Dic6—32no—
53C22×Dic6—32no—
54C22×Dic6—62no—
55C2×C3×C4⋊C4—32no—
56C2×C3×C42—21no—
57C2×C3×C42—31no—
58C2×C3×C42—31no—
59C2×C3×C42C2×D311yescharacteristic
60C2×C3×C42C2×D311yescharacteristic
61C2×C4⋊Dic3—34no—
62C2×C4⋊Dic3—34no—
63C2×C4⋊Dic3—64no—
64C2×C4⋊Dic3C2×D312yes—
65C2×Dic3⋊C4—34no—
66C2×Dic3⋊C4—34no—
67C2×C4×Dic3—34no—
68C2×C4×Dic3—34no—
69C2×C4×Dic3C2×D311yescharacteristic
70C2×C4×Dic3C2×D311yescharacteristic
71#887—68no—
72#869—38no—
73#869—38no—
74#869—68no—
75C4×Dic6—68no—
76C3×#95—34no—
77C3×#95—34no—
78C3⋊#95—38no—
79C3⋊#95—38no—
80C3⋊#95C2×D314yes—
81C3⋊#95C2×D314yes—
82C23×C32C2411yescharacteristic
83C2×C32×C4—24no—
84C2×C32×C4C22×C414yes—
85C2×C32×C4C22×C412yes—
86C2×C32×C4C2×D412yes—
87C2×C32×C4#4112yes—
88C2×C3⋊Dic3—24no—
89C2×C3⋊Dic3—24no—
90C2×C3⋊Dic3C22×C418yes—
91#634—216no—
92C2×C3×Dic3—24no—
93C2×C3×Dic3—24no—
94C2×C3×Dic3—22no—
95C2×C3×Dic3—28no—
96C2×C3×Dic3—24no—
97C2×C3×Dic3C2×D414yes—
98C2×C4⋊Q8—91no—
99C2×C4×Q8—92no—
100#391—92no—
101#387—98no—
102#382—31no—
103#376—31no—
104C22×C3×C4—22no—
105C22×C3×C4—21no—
106C22×C3×C4—32no—
107C22×C3×C4—32no—
108C22×C3×C4—34no—
109C22×C3×C4C22×D312yes—
110C22×C3×C4C22×D312yes—
111C22×C3×C4C22×D311yescharacteristic
112C22×C3×C4C22×D311yescharacteristic
113C22×Dic3—34no—
114C22×Dic3—34no—
115C22×Dic3—64no—
116C22×Dic3C22×D312yes—
117C22×Dic3C22×D314yes—
118C22×Dic3C22×D312yes—
119C2×Dic6—38no—
120C2×Dic6—38no—
121C2×Dic6—68no—
122C2×Dic6—64no—
123C2×Dic6—64no—
124C2×Dic6—64no—
125C2×Dic6—64no—
126C2×Dic6—124no—
127C2×Dic6—124no—
128C3×C4⋊C4—64no—
129C3×C42—24no—
130C3×C42—34no—
131C3×C42—62no—
132C3×C42C4×D314yes—
133C3×C42C4×D314yes—
134C4⋊Dic3—24no—
135C4⋊Dic3—316no—
136C4⋊Dic3—316no—
137C4⋊Dic3—616no—
138Dic3⋊C4—68no—
139Dic3⋊C4—68no—
140C4×Dic3—22no—
141C4×Dic3—68no—
142C4×Dic3—68no—
143C4×Dic3D1214yes—
144C22×C32C23×C411yescharacteristic
145C22×C32C22×D411yescharacteristic
146C22×C32C2×#4111yescharacteristic
147C22×C322−1+414yes—
148C32×C4—24no—
149C32×C4C4×D414yes—
150C3⋊Dic3—28no—
151C3×Dic3—24no—
152C3×Dic3—44no—
153C3×Dic3—42no—
154C22×Q8—92no—
155C4⋊Q8—98no—
156C4×Q8—188no—
157C2×C4⋊C4—32no—
158C2×C4⋊C4—94no—
159C2×C4⋊C4—94no—
160C2×C42—31no—
161C2×C42—31no—
162C2×C42—94no—
163C2×C42D3211yescharacteristic
164#95—34no—
165#95—34no—
166#95—98no—
167C23×C3—21no—
168C23×C3C23×D311yescharacteristic
169C23×C3C23×D311yescharacteristic
170C2×C3×C4—28no—
171C2×C3×C4—24no—
172C2×C3×C4—24no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—24no—
176C2×C3×C4—22no—
177C2×C3×C4—34no—
178C2×C3×C4—64no—
179C2×C3×C4—64no—
180C2×C3×C4—62no—
181C2×C3×C4—64no—
182C2×C3×C4—68no—
183C2×C3×C4C2×C4×D314yes—
184C2×C3×C4C2×C4×D314yes—
185C2×C3×C4C2×C4×D312yes—
186C2×C3×C4C2×C4×D312yes—
187C2×C3×C4C2×D1212yes—
188C2×C3×C4#23512yes—
189C2×C3×C4D3×D412yes—
190C2×C3×C4#23912yes—
191C2×Dic3—24no—
192C2×Dic3—22no—
193C2×Dic3—24no—
194C2×Dic3—28no—
195C2×Dic3—24no—
196C2×Dic3—38no—
197C2×Dic3—38no—
198C2×Dic3—68no—
199C2×Dic3—64no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—64no—
203C2×Dic3—124no—
204C2×Dic3—124no—
205C2×Dic3C2×D1214yes—
206Dic6—616no—
207Dic6—616no—
208Dic6—1216no—
209C2×C32C2×C4×D411yescharacteristic
210C2×C32#51912yes—
211C2×C32#53612yes—
212C2×C32#54112yes—
213C2×Q8—98no—
214C2×Q8—184no—
215C2×Q8—184no—
216C22×C4—32no—
217C22×C4—32no—
218C22×C4—34no—
219C22×C4—94no—
220C22×C4C2×D3212yes—
221C22×C4C2×D3211yescharacteristic
222C4⋊C4—64no—
223C4⋊C4—916no—
224C4⋊C4—188no—
225C42—34no—
226C42—62no—
227C42—188no—
228C42#62414yes—
229C22×C3—24no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3C22×C4×D311yescharacteristic
234C22×C3C22×C4×D311yescharacteristic
235C22×C3C22×D1211yescharacteristic
236C22×C3C2×#23511yescharacteristic
237C22×C3C2×D3×D411yescharacteristic
238C22×C3C2×#23911yescharacteristic
239C22×C3#101014yes—
240C22×C3#101014yes—
241C3×C4—28no—
242C3×C4—24no—
243C3×C4—24no—
244C3×C4—24no—
245C3×C4—64no—
246C3×C4—122no—
247C3×C4—124no—
248C3×C4C4×D1214yes—
249C3×C4#89314yes—
250Dic3—24no—
251Dic3—44no—
252Dic3—42no—
253Dic3—68no—
254Dic3—68no—
255Dic3—128no—
256C32#232711yescharacteristic, complemented, Sylow
257C23C22×D3211yescharacteristic
258Q8—1816no—
259C2×C4—24no—
260C2×C4—34no—
261C2×C4—64no—
262C2×C4—64no—
263C2×C4—68no—
264C2×C4—62no—
265C2×C4—64no—
266C2×C4—98no—
267C2×C4—184no—
268C2×C4—184no—
269C2×C4#379912yes—
270C2×C4D3×D1212yes—
271C2×C4C2×#62414yes—
272C2×C4C2×#62412yes—
273C2×C3—22no—
274C2×C3—22no—
275C2×C3—21no—
276C2×C3—22no—
277C2×C3C2×C4×D1211yescharacteristic
278C2×C3C2×#89311yescharacteristic
279C2×C3#551612yes—
280C2×C3#551612yes—
281C2×C3#551812yes—
282C2×C3#552612yes—
283C2×C3#567512yes—
284C2×C3#569812yes—
285C22#6429814yes—
286C22C2×#379911yescharacteristic
287C22C2×D3×D1211yescharacteristic
288C22C22×#62411yescharacteristic
289C4—24no—
290C4—64no—
291C4—122no—
292C4—124no—
293C4—188no—
294C4#6389414yes—
295C3—21no—
296C3#7338811yescharacteristic, complemented
297C3#7415211yescharacteristic, complemented
298C2#1059388112yes—
299C2#1059389412yes—
300C2#1059482812yes—
301C2C2×#6389411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2327
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
12. #64078C4semidirect
256. C32#2327semidirect
296. C3#73388semidirect
297. C3#74152semidirect

Maximal subgroups

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

subgroupindex
C2×#640782
C2×#638442
C3×#49362
C3×#49322
#105912712
#105912132
#741523
#733883