Finite Group Databasebeta

← #11805607

Subgroups — #11805607

Order 1152.

1201 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2C2×#63843C212yesmaximal
3C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
4C3×#4936C211yesmaximal, characteristic
5#10591357C212yesmaximal
6#10591268C214yesmaximal
7#10591242C212yesmaximal
8#10591206C212yesmaximal
9#82460—31nomaximal
10#74157—31nomaximal
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2212yes—
14C2×C4×C3⋊Dic3C2212yes—
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C3×C4×Dic6C418yescomplemented
20C2×Dic3⋊Dic3C2214yes—
21C2×Dic3⋊Dic3C2214yes—
22C2×Dic32C2214yes—
23#63843—28no—
24#63658C2211yescharacteristic
25#63658C2211yescharacteristic
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2212yes—
28#63579C2214yes—
29C2×C3×C4×Q8—31no—
30C2×Q8×Dic3—32no—
31C2×#887—32no—
32C2×C4×Dic6D311yescharacteristic
33C3×#382—31no—
34#4984—32no—
35#4984—34no—
36#4972—32no—
37#4936—32no—
38#4936D311yescharacteristic
39C4×C4⋊Dic3—31no—
40C4×C4⋊Dic3—31no—
41C4×C4⋊Dic3—32no—
42C4×C4⋊Dic3—61no—
43#4650—32no—
44#4649—32no—
45#4647—34no—
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2312yes—
50C22×C3⋊Dic3C2312yes—
51C22×C3×Dic3C2314yes—
52C22×C3×Dic3C2312yes—
53C22×C3×Dic3C2312yes—
54C2×C3×Dic6C2×C414yes—
55C2×C3×Dic6D414yes—
56C2×C3×Dic6Q814yes—
57C32×C42C2×C414yes—
58C4⋊(C3⋊Dic3)—24no—
59C4×C3⋊Dic3—24no—
60C3×C4⋊Dic3—24no—
61C3×C4⋊Dic3C2×C414yes—
62C3×Dic3⋊C4C2×C418yes—
63C3×C4×Dic3C2×C418yes—
64Dic3⋊Dic3—28no—
65Dic3⋊Dic3—28no—
66Dic32—28no—
67#2351—91noSylow
68C22×C3×Q8—31no—
69C22×Dic6C2×D311yescharacteristic
70C3×C4×Q8—38no—
71C2×C3×C4⋊C4—32no—
72C2×C3×C4⋊C4—31no—
73C2×C3×C4⋊C4—32no—
74C2×C3×C42—21no—
75C2×C3×C42—32no—
76C2×C3×C42C2×D311yescharacteristic
77C2×C3×C42C2×D311yescharacteristic
78Q8×Dic3—68no—
79C2×C4⋊Dic3—32no—
80C2×C4⋊Dic3—32no—
81C2×C4⋊Dic3—34no—
82C2×C4⋊Dic3—34no—
83C2×C4⋊Dic3—62no—
84C2×C4⋊Dic3C2×D312yes—
85C2×C4⋊Dic3C2×D311yescharacteristic
86C2×Dic3⋊C4—34no—
87C2×Dic3⋊C4—34no—
88C2×Dic3⋊C4C2×D312yes—
89C2×C4×Dic3—32no—
90C2×C4×Dic3—32no—
91C2×C4×Dic3—34no—
92C2×C4×Dic3—34no—
93C2×C4×Dic3—62no—
94C2×C4×Dic3C2×D312yes—
95#887—68no—
96C4×Dic6Dic318yescomplemented
97C3×#95—32no—
98C3×#95—32no—
99C3⋊#95—31no—
100C3⋊#95—31no—
101C3⋊#95—31no—
102C3⋊#95—31no—
103C3⋊#95—34no—
104C3⋊#95—34no—
105C3⋊#95—61no—
106C3⋊#95—61no—
107C3⋊#95C2×D312yes—
108C3⋊#95C2×D312yes—
109C23×C32C2411yescharacteristic
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4C22×C412yes—
113C2×C32×C4C22×C412yes—
114C2×C32×C4C22×C412yes—
115C2×C32×C4C2×D412yes—
116C2×C32×C4C2×Q812yes—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3#4114yes—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3C22×C414yes—
128C2×C3×Dic3C22×C414yes—
129C2×C3×Dic3C2×D414yes—
130C2×C3×Dic3C2×Q814yes—
131C3×Dic6C4⋊C4116yescomplemented
132C2×C4×Q8—31no—
133C2×C4×Q8—92no—
134#389—94no—
135#389—92no—
136#382—31no—
137#382—92no—
138C4×C4⋊C4—92no—
139C4×C4⋊C4—91no—
140C2×C3×Q8—34no—
141C2×C3×Q8—34no—
142C2×C3×Q8—34no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—32no—
147C22×C3×C4—32no—
148C22×C3×C4—34no—
149C22×C3×C4C22×D311yescharacteristic
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C22×Dic3—32no—
156C22×Dic3—32no—
157C22×Dic3—32no—
158C22×Dic3—32no—
159C22×Dic3—62no—
160C22×Dic3—62no—
161C22×Dic3C22×D314yes—
162C22×Dic3C22×D312yes—
163C22×Dic3C22×D312yes—
164C2×Dic6Dic614yes—
165C2×Dic6D1214yes—
166C2×Dic6C2×Dic314yes—
167C3×C4⋊C4—38no—
168C3×C4⋊C4—34no—
169C3×C4⋊C4—64no—
170C3×C42—24no—
171C3×C42—38no—
172C3×C42C4×D314yes—
173C3×C42C2×Dic314yes—
174C4⋊Dic3—24no—
175C4⋊Dic3—68no—
176C4⋊Dic3—68no—
177C4⋊Dic3—64no—
178C4⋊Dic3—64no—
179C4⋊Dic3—68no—
180C4⋊Dic3C2×Dic314yes—
181Dic3⋊C4—68no—
182Dic3⋊C4—68no—
183Dic3⋊C4C2×Dic318yes—
184C4×Dic3—68no—
185C4×Dic3—64no—
186C4×Dic3—64no—
187C4×Dic3—68no—
188C4×Dic3—124no—
189C4×Dic3C2×Dic318yes—
190C22×C32C23×C411yescharacteristic
191C22×C32C22×D411yescharacteristic
192C22×C32C22×Q811yescharacteristic
193C22×C32C2×#4112yes—
194C22×C322−1+412yes—
195C32×C4—22no—
196C32×C4—22no—
197C32×C4C2×C4⋊C414yes—
198C3⋊Dic3—24no—
199C3⋊Dic3—42no—
200C3×Dic3—24no—
201C3×Dic3—44no—
202C3×Dic3C2×C4⋊C418yes—
203C22×Q8—31no—
204C4×Q8—38no—
205C4×Q8—188no—
206C2×C4⋊C4—32no—
207C2×C4⋊C4—31no—
208C2×C4⋊C4—32no—
209C2×C4⋊C4—94no—
210C2×C4⋊C4—94no—
211C2×C4⋊C4—92no—
212C2×C42—32no—
213C2×C42—94no—
214C2×C42—92no—
215C2×C42D3211yescharacteristic
216#95—32no—
217#95—32no—
218#95—94no—
219#95—91no—
220#95—91no—
221C23×C3—21no—
222C23×C3C23×D311yescharacteristic
223C23×C3C23×D311yescharacteristic
224C3×Q8—316no—
225C2×C3×C4—24no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—34no—
236C2×C3×C4—34no—
237C2×C3×C4—34no—
238C2×C3×C4—34no—
239C2×C3×C4—42no—
240C2×C3×C4—64no—
241C2×C3×C4—64no—
242C2×C3×C4—64no—
243C2×C3×C4—64no—
244C2×C3×C4C2×Dic612yes—
245C2×C3×C4C2×C4×D312yes—
246C2×C3×C4C2×C4×D312yes—
247C2×C3×C4C2×C4×D312yes—
248C2×C3×C4C2×D1212yes—
249C2×C3×C4D3×D412yes—
250C2×C3×C4D3×Q812yes—
251C2×C3×C4C22×Dic312yes—
252C2×C3×C4C22×Dic312yes—
253C2×C3×C4C22×Dic312yes—
254C2×Dic3—24no—
255C2×Dic3—24no—
256C2×Dic3—24no—
257C2×Dic3—24no—
258C2×Dic3—34no—
259C2×Dic3—34no—
260C2×Dic3—64no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—64no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—62no—
269C2×Dic3—62no—
270C2×Dic3—62no—
271C2×Dic3—62no—
272C2×Dic3—122no—
273C2×Dic3—122no—
274C2×Dic3—122no—
275C2×Dic3—122no—
276C2×Dic3C2×Dic614yes—
277C2×Dic3C2×D1214yes—
278C2×Dic3C22×Dic314yes—
279C2×Dic3C22×Dic314yes—
280Dic6C4⋊Dic3116yescomplemented
281C2×C32C22×C4⋊C411yescharacteristic
282C2×C32C4×#4111yescharacteristic
283C2×C32#51911yescharacteristic
284C2×C32#54812yes—
285C2×C32#55712yes—
286C2×Q8—34no—
287C2×Q8—34no—
288C2×Q8—34no—
289C22×C4—32no—
290C22×C4—32no—
291C22×C4—34no—
292C22×C4—92no—
293C22×C4—92no—
294C22×C4C2×D3211yescharacteristic
295C22×C4C2×D3211yescharacteristic
296C22×C4C2×D3211yescharacteristic
297C4⋊C4—38no—
298C4⋊C4—34no—
299C4⋊C4—64no—
300C4⋊C4—184no—
301C4⋊C4—188no—
302C4⋊C4—188no—
303C42—38no—
304C42—188no—
305C42—184no—
306C42D3×Dic314yes—
307C22×C3—21no—
308C22×C3—22no—
309C22×C3—21no—
310C22×C3—22no—
311C22×C3—21no—
312C22×C3C22×Dic611yescharacteristic
313C22×C3C22×C4×D311yescharacteristic
314C22×C3C22×D1211yescharacteristic
315C22×C3C2×D3×D411yescharacteristic
316C22×C3C2×D3×Q811yescharacteristic
317C22×C3#100712yes—
318C22×C3D3×#4112yes—
319C22×C3D3×#4112yes—
320C22×C3#101012yes—
321C22×C3C23×Dic311yescharacteristic
322C3×C4—24no—
323C3×C4—22no—
324C3×C4—22no—
325C3×C4—22no—
326C3×C4—22no—
327C3×C4—24no—
328C3×C4—38no—
329C3×C4—42no—
330C3×C4—64no—
331C3×C4—124no—
332C3×C4D3×C4⋊C414yes—
333C3×C4C2×C4⋊Dic314yes—
334Dic3—24no—
335Dic3—44no—
336Dic3—64no—
337Dic3—64no—
338Dic3—124no—
339Dic3—124no—
340Dic3—122no—
341Dic3—122no—
342Dic3C2×C4⋊Dic318yes—
343C32#235111yescharacteristic, complemented, Sylow
344C23C22×D3211yescharacteristic
345Q8—316no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—34no—
349C2×C4—34no—
350C2×C4—34no—
351C2×C4—34no—
352C2×C4—64no—
353C2×C4—64no—
354C2×C4—64no—
355C2×C4—64no—
356C2×C4—94no—
357C2×C4—182no—
358C2×C4—182no—
359C2×C4—182no—
360C2×C4—182no—
361C2×C4—182no—
362C2×C4D3×Dic612yes—
363C2×C4D3×D1212yes—
364C2×C4C2×D3×Dic312yes—
365C2×C4C2×D3×Dic312yes—
366C2×C4C2×D3×Dic312yes—
367C2×C3—21no—
368C2×C3—22no—
369C2×C3—21no—
370C2×C3—22no—
371C2×C3—21no—
372C2×C3C2×D3×C4⋊C411yescharacteristic
373C2×C3#551611yescharacteristic
374C2×C3#552211yescharacteristic
375C2×C3#556912yes—
376C2×C3#557612yes—
377C2×C3#567712yes—
378C2×C3#568512yes—
379C2×C3C22×C4⋊Dic311yescharacteristic
380C2×C3#581211yescharacteristic
381C2×C3Dic3×#4111yescharacteristic
382C22C2×D3×Dic611yescharacteristic
383C22#6429712yes—
384C22C2×D3×D1211yescharacteristic
385C22#6430612yes—
386C22C22×D3×Dic311yescharacteristic
387C4—22no—
388C4—22no—
389C4—38no—
390C4—64no—
391C4—124no—
392C4—184no—
393C4—362no—
394C4D3×C4⋊Dic314yes—
395C3—21no—
396C3#7415711yescharacteristic, complemented
397C3#8246011yescharacteristic, complemented
398C2#1059385312yes—
399C2#1059390112yes—
400C2#1059481811yescharacteristic
401C2C2×D3×C4⋊Dic311yescharacteristic
402C2#1059495811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2351
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
19. C3×C4×Dic6C4semidirect
96. C4×Dic6Dic3semidirect
131. C3×Dic6C4⋊C4semidirect
280. Dic6C4⋊Dic3semidirect
343. C32#2351semidirect
396. C3#74157semidirect
397. C3#82460semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
C2×#638432
C4×C4⋊(C3⋊Dic3)2
C3×#49362
#105913572
#105912682
#105912422
#105912062
#824603
#741573