Finite Group Databasebeta

← #11805605

Subgroups — #11805605

Order 1152.

1181 conjugacy classes of subgroups.

The subgroup lattice has 397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2C2×Dic3×Dic6C212yesmaximal
3#10592635C211yesmaximal, characteristic
4C3×C4×C4⋊Dic3C211yesmaximal, characteristic
5#10591352C212yesmaximal
6#10591265C214yesmaximal
7#10591242C212yesmaximal
8#10591206C212yesmaximal
9#82460—31nomaximal
10#73637—31nomaximal
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2212yes—
14C2×C3×C4⋊Dic3C2212yes—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×Dic3⋊C4C2212yes—
17C2×C3×C4×Dic3C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C3×C4×Dic6C418yescomplemented
20C2×Dic3⋊Dic3C2214yes—
21C2×Dic3⋊Dic3C2214yes—
22C2×Dic32C2214yes—
23Dic3×Dic6—28no—
24#63658C2212yes—
25#63658C2212yes—
26C3×C3⋊#95C2211yescharacteristic
27C3×C3⋊#95C2211yescharacteristic
28#63579C2214yes—
29C2×C3×C4×Q8—31no—
30C2×Q8×Dic3—32no—
31C2×C4×Dic6—32no—
32C2×C4×Dic6D311yescharacteristic
33C3×C4×C4⋊C4—31no—
34#4984—34no—
35#4984—32no—
36#4976—34no—
37#4936—31no—
38#4936—31no—
39#4936—32no—
40#4936—61no—
41C4×C4⋊Dic3—32no—
42C4×C4⋊Dic3D311yescharacteristic
43#4928—32no—
44#4650—32no—
45#4649—32no—
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2314yes—
50C22×C3×Dic3C2312yes—
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2312yes—
53C22×C3×Dic3C2312yes—
54C2×C3×Dic6C2×C414yes—
55C2×C3×Dic6D414yes—
56C2×C3×Dic6Q814yes—
57C32×C42C2×C414yes—
58C4⋊(C3⋊Dic3)—24no—
59C3×C4⋊Dic3—24no—
60C3×C4⋊Dic3C2×C414yes—
61C3×Dic3⋊C4C2×C418yes—
62C3×C4×Dic3—24no—
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×C42—32no—
77C2×C3×C42C2×D311yescharacteristic
78C2×C3×C42C2×D311yescharacteristic
79Q8×Dic3—68no—
80C2×C4⋊Dic3—32no—
81C2×C4⋊Dic3—32no—
82C2×C4⋊Dic3—34no—
83C2×C4⋊Dic3—34no—
84C2×C4⋊Dic3—62no—
85C2×C4⋊Dic3C2×D312yes—
86C2×C4⋊Dic3C2×D311yescharacteristic
87C2×Dic3⋊C4—34no—
88C2×Dic3⋊C4—34no—
89C2×Dic3⋊C4C2×D312yes—
90C2×C4×Dic3—34no—
91C2×C4×Dic3—34no—
92C2×C4×Dic3C2×D312yes—
93C2×C4×Dic3C2×D312yes—
94C4×Dic6—68no—
95C4×Dic6Dic318yescomplemented
96C3×#95—31no—
97C3×#95—31no—
98C3⋊#95—32no—
99C3⋊#95—32no—
100C3⋊#95—32no—
101C3⋊#95—32no—
102C3⋊#95—34no—
103C3⋊#95—34no—
104C3⋊#95—62no—
105C3⋊#95—62no—
106C3⋊#95C2×D311yescharacteristic
107C3⋊#95C2×D311yescharacteristic
108C23×C32C2411yescharacteristic
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4C22×C412yes—
112C2×C32×C4C22×C412yes—
113C2×C32×C4C22×C412yes—
114C2×C32×C4C2×D412yes—
115C2×C32×C4C2×Q812yes—
116C2×C3⋊Dic3—24no—
117C2×C3⋊Dic3—24no—
118C2×C3⋊Dic3—24no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3C22×C414yes—
126C2×C3×Dic3C22×C414yes—
127C2×C3×Dic3C2×D414yes—
128C2×C3×Dic3C2×Q814yes—
129C2×C3×Dic3#4114yes—
130C3×Dic6C4⋊C4116yescomplemented
131C2×C4×Q8—31no—
132C2×C4×Q8—92no—
133#389—92no—
134#389—94no—
135#382—92no—
136#382—91no—
137C4×C4⋊C4—31no—
138C4×C4⋊C4—92no—
139C2×C3×Q8—34no—
140C2×C3×Q8—34no—
141C2×C3×Q8—34no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—32no—
146C22×C3×C4—32no—
147C22×C3×C4—32no—
148C22×C3×C4—32no—
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—34no—
156C22×Dic3—34no—
157C22×Dic3—64no—
158C22×Dic3C22×D312yes—
159C22×Dic3C22×D312yes—
160C22×Dic3C22×D312yes—
161C22×Dic3C22×D312yes—
162C2×Dic6Dic614yes—
163C2×Dic6D1214yes—
164C2×Dic6C2×Dic314yes—
165C3×C4⋊C4—38no—
166C3×C4⋊C4—34no—
167C3×C4⋊C4—64no—
168C3×C42—24no—
169C3×C42—38no—
170C3×C42—64no—
171C3×C42C4×D314yes—
172C3×C42C2×Dic314yes—
173C4⋊Dic3—24no—
174C4⋊Dic3—68no—
175C4⋊Dic3—64no—
176C4⋊Dic3—64no—
177C4⋊Dic3—68no—
178C4⋊Dic3—124no—
179C4⋊Dic3C2×Dic314yes—
180Dic3⋊C4—68no—
181Dic3⋊C4—68no—
182Dic3⋊C4C2×Dic318yes—
183C4×Dic3—24no—
184C4×Dic3—68no—
185C4×Dic3—68no—
186C4×Dic3C2×Dic318yes—
187C22×C32C23×C411yescharacteristic
188C22×C32C22×D411yescharacteristic
189C22×C32C22×Q811yescharacteristic
190C22×C32C2×#4112yes—
191C22×C322−1+412yes—
192C32×C4—22no—
193C32×C4—22no—
194C32×C4C2×C4⋊C414yes—
195C3⋊Dic3—44no—
196C3×Dic3—24no—
197C3×Dic3—24no—
198C3×Dic3—42no—
199C3×Dic3C2×C4⋊C418yes—
200C22×Q8—31no—
201C4×Q8—38no—
202C4×Q8—188no—
203C2×C4⋊C4—32no—
204C2×C4⋊C4—31no—
205C2×C4⋊C4—32no—
206C2×C4⋊C4—94no—
207C2×C4⋊C4—94no—
208C2×C4⋊C4—92no—
209C2×C42—32no—
210C2×C42—32no—
211C2×C42—94no—
212C2×C42D3211yescharacteristic
213#95—31no—
214#95—31no—
215#95—94no—
216#95—92no—
217#95—92no—
218C23×C3—21no—
219C23×C3C23×D311yescharacteristic
220C23×C3C23×D311yescharacteristic
221C3×Q8—316no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—34no—
232C2×C3×C4—34no—
233C2×C3×C4—34no—
234C2×C3×C4—34no—
235C2×C3×C4—34no—
236C2×C3×C4—42no—
237C2×C3×C4—42no—
238C2×C3×C4—62no—
239C2×C3×C4—64no—
240C2×C3×C4—62no—
241C2×C3×C4—62no—
242C2×C3×C4—62no—
243C2×C3×C4—62no—
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—22no—
255C2×Dic3—24no—
256C2×Dic3—22no—
257C2×Dic3—22no—
258C2×Dic3—22no—
259C2×Dic3—22no—
260C2×Dic3—64no—
261C2×Dic3—64no—
262C2×Dic3—64no—
263C2×Dic3—64no—
264C2×Dic3—64no—
265C2×Dic3—64no—
266C2×Dic3—124no—
267C2×Dic3—124no—
268C2×Dic3—124no—
269C2×Dic3C2×Dic614yes—
270C2×Dic3C2×D1214yes—
271C2×Dic3#23514yes—
272C2×Dic3C22×Dic314yes—
273C2×Dic3C22×Dic314yes—
274Dic6C4⋊Dic3116yescomplemented
275C2×C32C22×C4⋊C411yescharacteristic
276C2×C32C4×#4111yescharacteristic
277C2×C32#51911yescharacteristic
278C2×C32#54812yes—
279C2×C32#55712yes—
280C2×Q8—34no—
281C2×Q8—34no—
282C2×Q8—34no—
283C22×C4—32no—
284C22×C4—32no—
285C22×C4—32no—
286C22×C4—32no—
287C22×C4—94no—
288C22×C4C2×D3211yescharacteristic
289C22×C4C2×D3211yescharacteristic
290C22×C4C2×D3211yescharacteristic
291C4⋊C4—38no—
292C4⋊C4—34no—
293C4⋊C4—64no—
294C4⋊C4—188no—
295C4⋊C4—188no—
296C4⋊C4—184no—
297C42—38no—
298C42—64no—
299C42—188no—
300C42D3×Dic314yes—
301C22×C3—21no—
302C22×C3—22no—
303C22×C3—21no—
304C22×C3—22no—
305C22×C3—21no—
306C22×C3C22×Dic611yescharacteristic
307C22×C3C22×C4×D311yescharacteristic
308C22×C3C22×D1211yescharacteristic
309C22×C3C2×#23512yes—
310C22×C3C2×D3×D411yescharacteristic
311C22×C3C2×D3×Q811yescharacteristic
312C22×C3#100712yes—
313C22×C3D3×#4112yes—
314C22×C3#101012yes—
315C22×C3C23×Dic311yescharacteristic
316C3×C4—22no—
317C3×C4—22no—
318C3×C4—22no—
319C3×C4—22no—
320C3×C4—24no—
321C3×C4—38no—
322C3×C4—42no—
323C3×C4—42no—
324C3×C4—64no—
325C3×C4—64no—
326C3×C4—122no—
327C3×C4D3×C4⋊C414yes—
328C3×C4C2×C4⋊Dic314yes—
329Dic3—24no—
330Dic3—24no—
331Dic3—42no—
332Dic3—124no—
333Dic3—124no—
334Dic3—244no—
335Dic3C2×C4⋊Dic318yes—
336C32#235111yescharacteristic, complemented, Sylow
337C23C22×D3211yescharacteristic
338Q8—316no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—34no—
342C2×C4—34no—
343C2×C4—34no—
344C2×C4—34no—
345C2×C4—34no—
346C2×C4—62no—
347C2×C4—62no—
348C2×C4—64no—
349C2×C4—62no—
350C2×C4—62no—
351C2×C4—62no—
352C2×C4—184no—
353C2×C4—184no—
354C2×C4—184no—
355C2×C4D3×Dic612yes—
356C2×C4D3×D1212yes—
357C2×C4C2×D3×Dic312yes—
358C2×C4C2×D3×Dic312yes—
359C2×C4C2×D3×Dic312yes—
360C2×C3—21no—
361C2×C3—22no—
362C2×C3—21no—
363C2×C3—22no—
364C2×C3—21no—
365C2×C3C4×#23511yescharacteristic
366C2×C3C2×D3×C4⋊C411yescharacteristic
367C2×C3#551611yescharacteristic
368C2×C3#555212yes—
369C2×C3#556712yes—
370C2×C3#556912yes—
371C2×C3#557612yes—
372C2×C3C22×C4⋊Dic311yescharacteristic
373C2×C3#581211yescharacteristic
374C2×C3Dic3×#4111yescharacteristic
375C22C2×D3×Dic611yescharacteristic
376C22#6429712yes—
377C22C2×D3×D1211yescharacteristic
378C22D3×#23512yes—
379C22C22×D3×Dic311yescharacteristic
380C4—22no—
381C4—22no—
382C4—38no—
383C4—64no—
384C4—64no—
385C4—122no—
386C4—364no—
387C4D3×C4⋊Dic314yes—
388C3—21no—
389C3#7363711yescharacteristic, complemented
390C3#8246011yescharacteristic, complemented
391C2#1059385112yes—
392C2#1059389912yes—
393C2#1059481811yescharacteristic
394C2C2×D3×C4⋊Dic311yescharacteristic
395C2Dic3×#23511yescharacteristic
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
95. C4×Dic6Dic3semidirect
130. C3×Dic6C4⋊C4semidirect
274. Dic6C4⋊Dic3semidirect
336. C32#2351semidirect
389. C3#73637semidirect
390. 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×Dic3×Dic62
#105926352
C3×C4×C4⋊Dic32
#105913522
#105912652
#105912422
#105912062
#824603
#736373