Finite Group Databasebeta

← #11795083

Subgroups — #11795083

Order 1152.

519 conjugacy classes of subgroups.

The subgroup lattice has 349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#4935C211yesmaximal, characteristic
2C3×#4928C211yesmaximal, characteristic
3C2×#63576C212yesmaximal
4#10589390C211yesmaximal, characteristic
5#10589163C212yesmaximal
6#69607—31nomaximal
7#69569—31nomaximal
8C2×C32×C42C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2212yes—
10C2×C3×C4⋊Dic3—21no—
11C2×C3×C4⋊Dic3—21no—
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C2×C3×C4⋊Dic3C2212yes—
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×Dic3⋊C4—21no—
16C3×C3⋊#95—21no—
17#63576—24no—
18C3×#389—31no—
19C3×#384—31no—
20C2×#807—32no—
21C2×#807—32no—
22#4935D311yescharacteristic
23#4928D311yescharacteristic
24#4529—32no—
25#4529—32no—
26#4524—31no—
27#4524—31no—
28#4524—61no—
29C22×C32×C4D411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4C2311yescharacteristic
32C22×C3×Dic3—21no—
33C22×C3×Dic3—21no—
34C22×C3×Dic3—22no—
35C32×C42—22no—
36C2×C3⋊(C3⋊C8)—22no—
37C2×C3⋊(C3⋊C8)—22no—
38C2×C3⋊(C3⋊C8)Q814yes—
39C3×C4⋊Dic3—21no—
40C3×C4⋊Dic3—22no—
41C3×C4⋊Dic3—22no—
42C3×C4⋊Dic3—22no—
43C3×C4⋊Dic3—42no—
44C3×C4⋊Dic3—42no—
45C3×C4⋊Dic3D412yes—
46C3×Dic3⋊C4—42no—
47#2083—91noSylow
48C2×C3×C4⋊C4—31no—
49C2×C3×C4⋊C4—32no—
50C2×C3×C4⋊C4—31no—
51C2×C3×C4⋊C4—61no—
52C2×C3×C4⋊C4—61no—
53C2×C3×C4⋊C4—61no—
54C2×C3×C42—21no—
55C2×C3×C42C2×D311yescharacteristic
56C2×C3×C42C2×D311yescharacteristic
57C2×C4⋊Dic3—21no—
58C2×C4⋊Dic3—21no—
59C2×C4⋊Dic3C2×D311yescharacteristic
60C2×C4⋊Dic3C2×D312yes—
61C2×C4⋊Dic3C2×D311yescharacteristic
62C2×Dic3⋊C4—21no—
63C22×C3⋊C8—32no—
64C22×C3⋊C8—32no—
65C22×C3⋊C8—62no—
66C3×#95—61no—
67C3⋊#95—21no—
68#807—64no—
69#807—64no—
70C23×C32C2×D411yescharacteristic
71C2×C32×C4—21no—
72C2×C32×C4—21no—
73C2×C32×C4—21no—
74C2×C32×C4—21no—
75C2×C32×C4D812yes—
76C2×C32×C4Q1612yes—
77C2×C32×C4C2×D411yescharacteristic
78C2×C32×C4C2×Q812yes—
79C2×C32×C4#4112yes—
80C2×C32×C4#4111yescharacteristic
81C2×C3×Dic3—22no—
82C2×C3×Dic3—41no—
83C2×C3×Dic3—41no—
84C2×C3×Dic3—42no—
85C2×C3×Dic3—41no—
86C2×C3×Dic3—41no—
87C2×C3×Dic3—42no—
88C2×C3×Dic3—42no—
89C2×C3×Dic3—41no—
90C3⋊(C3⋊C8)—24no—
91C2×#107—92no—
92#389—31no—
93#384—31no—
94#340—92no—
95#336—91no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C22×C3×C4—61no—
100C22×C3×C4—61no—
101C22×C3×C4—62no—
102C22×C3×C4#6711yescharacteristic
103C22×C3×C4#6711yescharacteristic
104C22×C3×C4#6711yescharacteristic
105C22×C3×C4#6711yescharacteristic
106C22×C3×C4C22×D311yescharacteristic
107C22×C3×C4C22×D311yescharacteristic
108C22×Dic3—21no—
109C22×Dic3—21no—
110C22×Dic3—22no—
111C3×C4⋊C4—32no—
112C3×C4⋊C4—61no—
113C3×C4⋊C4—62no—
114C3×C4⋊C4—62no—
115C3×C4⋊C4—62no—
116C3×C4⋊C4—122no—
117C3×C4⋊C4—122no—
118C3×C4⋊C4—122no—
119C3×C42—22no—
120C3×C42—22no—
121C3×C42—42no—
122C4⋊Dic3—21no—
123C4⋊Dic3—22no—
124C4⋊Dic3—22no—
125C4⋊Dic3—22no—
126C4⋊Dic3—42no—
127C4⋊Dic3—42no—
128C4⋊Dic3D1212yes—
129Dic3⋊C4—42no—
130C2×C3⋊C8—34no—
131C2×C3⋊C8—34no—
132C2×C3⋊C8—64no—
133C2×C3⋊C8—62no—
134C2×C3⋊C8—62no—
135C2×C3⋊C8—62no—
136C2×C3⋊C8—62no—
137C2×C3⋊C8—122no—
138C2×C3⋊C8—122no—
139C22×C32#12111yescharacteristic
140C22×C32#12311yescharacteristic
141C22×C32C4⋊Q811yescharacteristic
142C22×C32C2×D811yescharacteristic
143C22×C32C2×Q1611yescharacteristic
144C22×C32AGL(1,ℤ/8)11yescharacteristic
145C22×C32#13711yescharacteristic
146C32×C4—22no—
147C32×C4—22no—
148C32×C4C22⋊Q812yes—
149C32×C4#12512yes—
150C3×Dic3—42no—
151C3×Dic3—82no—
152C3×Dic3—81no—
153C22×C8—92no—
154C2×C4⋊C4—31no—
155C2×C4⋊C4—31no—
156C2×C4⋊C4—32no—
157C2×C4⋊C4—61no—
158C2×C4⋊C4—61no—
159C2×C4⋊C4—61no—
160C2×C42D3211yescharacteristic
161#107—184no—
162#95—61no—
163C23×C3—21no—
164C23×C3C2×#6711yescharacteristic
165C23×C3C2×#6711yescharacteristic
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—21no—
177C2×C3×C4—22no—
178C2×C3×C4—21no—
179C2×C3×C4—22no—
180C2×C3×C4—41no—
181C2×C3×C4—41no—
182C2×C3×C4—41no—
183C2×C3×C4—41no—
184C2×C3×C4—62no—
185C2×C3×C4—121no—
186C2×C3×C4—121no—
187C2×C3×C4—121no—
188C2×C3×C4—122no—
189C2×C3×C4—121no—
190C2×C3×C4—122no—
191C2×C3×C4—121no—
192C2×C3×C4—122no—
193C2×C3×C4#21312yes—
194C2×C3×C4#21312yes—
195C2×C3×C4#21612yes—
196C2×C3×C4#21612yes—
197C2×C3×C4C2×D1211yescharacteristic
198C2×C3×C4#23511yescharacteristic
199C2×C3×C4#23512yes—
200C2×C3×C4D3×D411yescharacteristic
201C2×C3×C4#23711yescharacteristic
202C2×C3×C4#23712yes—
203C2×C3×C4D3×Q812yes—
204C2×C3×C4D3×Q812yes—
205C2×Dic3—22no—
206C2×Dic3—41no—
207C2×Dic3—41no—
208C2×Dic3—41no—
209C2×Dic3—42no—
210C2×Dic3—42no—
211C2×Dic3—41no—
212C2×Dic3—42no—
213C2×Dic3—41no—
214C3⋊C8—64no—
215C3⋊C8—64no—
216C3⋊C8—124no—
217C2×C32#39811yescharacteristic
218C2×C32#45911yescharacteristic
219C2×C32#46211yescharacteristic
220C2×C32#48011yescharacteristic
221C2×C32#48411yescharacteristic
222C2×C32#50011yescharacteristic
223C2×C32#50111yescharacteristic
224C22×C4—61no—
225C22×C4—61no—
226C22×C4—62no—
227C22×C4#62511yescharacteristic
228C22×C4#62511yescharacteristic
229C22×C4C2×D3211yescharacteristic
230C2×C8—94no—
231C2×C8—182no—
232C2×C8—182no—
233C4⋊C4—32no—
234C4⋊C4—61no—
235C4⋊C4—62no—
236C4⋊C4—62no—
237C4⋊C4—62no—
238C4⋊C4—122no—
239C4⋊C4—122no—
240C4⋊C4—122no—
241C42—22no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3#92911yescharacteristic
250C22×C3#93011yescharacteristic
251C22×C3C2×#21311yescharacteristic
252C22×C3C2×#21311yescharacteristic
253C22×C3#93211yescharacteristic
254C22×C3#93511yescharacteristic
255C22×C3#93811yescharacteristic
256C22×C3#94211yescharacteristic
257C22×C3C2×#21611yescharacteristic
258C22×C3C2×#21611yescharacteristic
259C22×C3#94411yescharacteristic
260C22×C3#94411yescharacteristic
261C22×C3#94911yescharacteristic
262C22×C3#95111yescharacteristic
263C3×C4—22no—
264C3×C4—22no—
265C3×C4—22no—
266C3×C4—22no—
267C3×C4—22no—
268C3×C4—22no—
269C3×C4—42no—
270C3×C4—42no—
271C3×C4—122no—
272C3×C4—241no—
273C3×C4—242no—
274C3×C4#88912yes—
275C3×C4#88912yes—
276C3×C4#89612yes—
277C3×C4#89712yes—
278Dic3—42no—
279Dic3—81no—
280Dic3—82no—
281C32#208311yescharacteristic, complemented, Sylow
282C23C2×#62511yescharacteristic
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—62no—
288C2×C4—121no—
289C2×C4—121no—
290C2×C4—121no—
291C2×C4—122no—
292C2×C4—122no—
293C2×C4—121no—
294C2×C4—122no—
295C2×C4—121no—
296C2×C4#371312yes—
297C2×C4#371812yes—
298C2×C4#379511yescharacteristic
299C2×C4#379712yes—
300C2×C4D3×D1211yescharacteristic
301C2×C4#380412yes—
302C8—184no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3#496711yescharacteristic
311C2×C3#497011yescharacteristic
312C2×C3#498111yescharacteristic
313C2×C3#498311yescharacteristic
314C2×C3#501511yescharacteristic
315C2×C3#503111yescharacteristic
316C2×C3#503311yescharacteristic
317C2×C3#504411yescharacteristic
318C2×C3#506411yescharacteristic
319C2×C3#507211yescharacteristic
320C2×C3#507811yescharacteristic
321C2×C3#507811yescharacteristic
322C2×C3#508111yescharacteristic
323C2×C3#509011yescharacteristic
324C22C2×#371311yescharacteristic
325C22#6382311yescharacteristic
326C22#6382711yescharacteristic
327C22C2×#371811yescharacteristic
328C22#6387311yescharacteristic
329C22#6390811yescharacteristic
330C22#6396111yescharacteristic
331C4—22no—
332C4—22no—
333C4—122no—
334C4—241no—
335C4—242no—
336C4#6384712yes—
337C4#6389512yes—
338C3—21no—
339C3#6956911yescharacteristic, complemented
340C3#6960711yescharacteristic, complemented
341C2#1059031211yescharacteristic
342C2#1059031511yescharacteristic
343C2#1059034711yescharacteristic
344C2#1059038411yescharacteristic
345C2#1059108911yescharacteristic
346C2#1059113211yescharacteristic
347C2#1059121411yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C2×D4
hypercenterC2×C42D32
hypocenterC32#2083
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
281. C32#2083semidirect
339. C3#69569semidirect
340. C3#69607semidirect

Maximal subgroups

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

subgroupindex
C3×#49352
C3×#49282
C2×#635762
#105893902
#105891632
#696073
#695693