Finite Group Databasebeta

← #11803212

Subgroups — #11803212

Order 1152.

977 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2#10592631C211yesmaximal, characteristic
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic
4#10591357C212yesmaximal
5#10591223C212yesmaximal
6#10591221C212yesmaximal
7#10591206C212yesmaximal
8#10591201C214yesmaximal
9#82454—31nomaximal
10#73625—31nomaximal
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4×C3⋊Dic3C2212yes—
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—
21#63658C2212yes—
22#63658C2211yescharacteristic
23#63658C2211yescharacteristic
24C3×C3⋊#95C2212yes—
25#63579C2214yes—
26#63579C2214yes—
27#63579C2214yes—
28C2×C3×C4×Q8—31no—
29C2×C4×Dic6D311yescharacteristic
30C3×C4×C4⋊C4—31no—
31#5229—32no—
32#4984—32no—
33#4980—34no—
34#4973—32no—
35#4972—32no—
36#4937—32no—
37#4936—32no—
38C4×C4⋊Dic3D311yescharacteristic
39#4933—34no—
40#4932—31no—
41#4932—31no—
42#4932—61no—
43#4651—32no—
44#4650—32no—
45C22×C32×C4C2311yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3C2312yes—
49C22×C3⋊Dic3C2312yes—
50C22×C3×Dic3C2314yes—
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2312yes—
53C2×C3×Dic6—24no—
54C2×C3×Dic6C2×C414yes—
55C32×C42C2×C414yes—
56C4×C3⋊Dic3—24no—
57C3×C4⋊Dic3—24no—
58C3×C4⋊Dic3C2×C414yes—
59C3×Dic3⋊C4C2×C418yes—
60C3×C4×Dic3—42no—
61C3×C4×Dic3C2×C418yes—
62Dic3⋊Dic3—44no—
63#2320—91noSylow
64C22×C3×Q8—31no—
65C22×Dic6C2×D311yescharacteristic
66C3×C4×Q8—38no—
67C2×C3×C4⋊C4—32no—
68C2×C3×C4⋊C4—31no—
69C2×C3×C4⋊C4—32no—
70C2×C3×C42—21no—
71C2×C3×C42—32no—
72C2×C3×C42—32no—
73C2×C3×C42C2×D311yescharacteristic
74C2×C3×C42C2×D311yescharacteristic
75C2×C4⋊Dic3—34no—
76C2×C4⋊Dic3C2×D312yes—
77C2×C4⋊Dic3C2×D311yescharacteristic
78C2×Dic3⋊C4—34no—
79C2×Dic3⋊C4C2×D312yes—
80C2×C4×Dic3—32no—
81C2×C4×Dic3—32no—
82C2×C4×Dic3—62no—
83C2×C4×Dic3C2×D312yes—
84C2×C4×Dic3C2×D312yes—
85C4×Dic6Dic318yescomplemented
86C3×#95—32no—
87C3⋊#95—31no—
88C3⋊#95—31no—
89C3⋊#95—32no—
90C3⋊#95—31no—
91C3⋊#95—31no—
92C3⋊#95—32no—
93C3⋊#95—34no—
94C3⋊#95—34no—
95C3⋊#95—34no—
96C3⋊#95—34no—
97C3⋊#95—34no—
98C3⋊#95—34no—
99C3⋊#95—61no—
100C3⋊#95—61no—
101C3⋊#95—62no—
102C3⋊#95C2×D312yes—
103C23×C32C2411yescharacteristic
104C2×C32×C4—21no—
105C2×C32×C4—22no—
106C2×C32×C4—21no—
107C2×C32×C4C22×C412yes—
108C2×C32×C4C22×C412yes—
109C2×C32×C4C22×C412yes—
110C2×C32×C4#4114yes—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—24no—
122C2×C3×Dic3—24no—
123C2×C3×Dic3C22×C414yes—
124C2×C3×Dic3C22×C414yes—
125C3×Dic6—28no—
126C2×C4×Q8—31no—
127#391—92no—
128#389—92no—
129#387—94no—
130#383—92no—
131#382—92no—
132C4×C4⋊C4—31no—
133#376—91no—
134C2×C3×Q8—34no—
135C2×C3×Q8—64no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—32no—
140C22×C3×C4—32no—
141C22×C3×C4—34no—
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C22×C3×C4C22×D311yescharacteristic
147C22×C3×C4C22×D311yescharacteristic
148C22×Dic3—32no—
149C22×Dic3—32no—
150C22×Dic3—32no—
151C22×Dic3—32no—
152C22×Dic3—62no—
153C22×Dic3—62no—
154C22×Dic3C22×D314yes—
155C22×Dic3C22×D312yes—
156C22×Dic3C22×D312yes—
157C2×Dic6—24no—
158C2×Dic6C2×Dic314yes—
159C3×C4⋊C4—38no—
160C3×C4⋊C4—34no—
161C3×C4⋊C4—64no—
162C3×C42—24no—
163C3×C42—38no—
164C3×C42—122no—
165C3×C42C4×D314yes—
166C3×C42C2×Dic314yes—
167C4⋊Dic3—24no—
168C4⋊Dic3—124no—
169C4⋊Dic3C2×Dic314yes—
170Dic3⋊C4—124no—
171Dic3⋊C4C2×Dic318yes—
172C4×Dic3—42no—
173C4×Dic3—68no—
174C4×Dic3—64no—
175C4×Dic3—64no—
176C4×Dic3C2×Dic318yes—
177C22×C32C23×C411yescharacteristic
178C22×C32C2×#4112yes—
179C22×C32H(5,𝔽2)11yescharacteristic
180C22×C322−1+412yes—
181C22×C322−1+411yescharacteristic
182C32×C4—22no—
183C32×C4—22no—
184C32×C4#11714yes—
185C3⋊Dic3—42no—
186C3⋊Dic3—42no—
187C3×Dic3—24no—
188C3×Dic3—24no—
189C3×Dic3—44no—
190C22×Q8—31no—
191C4×Q8—38no—
192C2×C4⋊C4—32no—
193C2×C4⋊C4—31no—
194C2×C4⋊C4—32no—
195C2×C4⋊C4—94no—
196C2×C42—32no—
197C2×C42—32no—
198C2×C42—92no—
199C2×C42D3211yescharacteristic
200#95—32no—
201#95—94no—
202#95—94no—
203#95—94no—
204#95—91no—
205#95—91no—
206#95—92no—
207C23×C3—21no—
208C23×C3C23×D311yescharacteristic
209C23×C3C23×D311yescharacteristic
210C3×Q8—68no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—22no—
214C2×C3×C4—21no—
215C2×C3×C4—22no—
216C2×C3×C4—21no—
217C2×C3×C4—24no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—22no—
221C2×C3×C4—34no—
222C2×C3×C4—34no—
223C2×C3×C4—42no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—64no—
227C2×C3×C4—62no—
228C2×C3×C4—62no—
229C2×C3×C4—64no—
230C2×C3×C4—64no—
231C2×C3×C4—64no—
232C2×C3×C4C2×C4×D312yes—
233C2×C3×C4C2×C4×D312yes—
234C2×C3×C4C2×C4×D312yes—
235C2×C3×C4#23514yes—
236C2×C3×C4#23514yes—
237C2×C3×C4C22×Dic312yes—
238C2×C3×C4C22×Dic312yes—
239C2×C3×C4C22×Dic312yes—
240C2×Dic3—24no—
241C2×Dic3—22no—
242C2×Dic3—22no—
243C2×Dic3—24no—
244C2×Dic3—24no—
245C2×Dic3—24no—
246C2×Dic3—64no—
247C2×Dic3—64no—
248C2×Dic3—62no—
249C2×Dic3—62no—
250C2×Dic3—62no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254C2×Dic3—62no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—62no—
258C2×Dic3—62no—
259C2×Dic3—62no—
260C2×Dic3—122no—
261C2×Dic3—122no—
262C2×Dic3—122no—
263C2×Dic3—122no—
264C2×Dic3C22×Dic314yes—
265C2×Dic3C22×Dic314yes—
266Dic6—28no—
267C2×C32C2×#11711yescharacteristic
268C2×C32#51911yescharacteristic
269C2×C32#52011yescharacteristic
270C2×C32#54112yes—
271C2×C32#54212yes—
272C2×Q8—34no—
273C2×Q8—64no—
274C22×C4—32no—
275C22×C4—32no—
276C22×C4—34no—
277C22×C4—92no—
278C22×C4—92no—
279C22×C4C2×D3211yescharacteristic
280C22×C4C2×D3211yescharacteristic
281C22×C4C2×D3211yescharacteristic
282C4⋊C4—38no—
283C4⋊C4—34no—
284C4⋊C4—64no—
285C4⋊C4—364no—
286C42—38no—
287C42—122no—
288C42—184no—
289C42D3×Dic314yes—
290C22×C3—22no—
291C22×C3—21no—
292C22×C3—22no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3C22×C4×D311yescharacteristic
296C22×C3C2×#23512yes—
297C22×C3C2×#23512yes—
298C22×C3#100411yescharacteristic
299C22×C3#100711yescharacteristic
300C22×C3#100712yes—
301C22×C3#100911yescharacteristic
302C22×C3#101012yes—
303C22×C3#101011yescharacteristic
304C22×C3C23×Dic311yescharacteristic
305C3×C4—22no—
306C3×C4—22no—
307C3×C4—22no—
308C3×C4—22no—
309C3×C4—24no—
310C3×C4—42no—
311C3×C4—42no—
312C3×C4—64no—
313C3×C4—64no—
314C3×C4—124no—
315C3×C4#87214yes—
316C3×C4#92614yes—
317Dic3—24no—
318Dic3—24no—
319Dic3—44no—
320Dic3—124no—
321Dic3—124no—
322Dic3—122no—
323Dic3—122no—
324Dic3—122no—
325Dic3—122no—
326C32#232011yescharacteristic, complemented, Sylow
327C23C22×D3211yescharacteristic
328Q8—68no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—34no—
333C2×C4—34no—
334C2×C4—62no—
335C2×C4—64no—
336C2×C4—62no—
337C2×C4—64no—
338C2×C4—64no—
339C2×C4—64no—
340C2×C4—182no—
341C2×C4—182no—
342C2×C4—182no—
343C2×C4—182no—
344C2×C4—182no—
345C2×C4—182no—
346C2×C4#379814yes—
347C2×C4C2×D3×Dic312yes—
348C2×C4C2×D3×Dic312yes—
349C2×C4C2×D3×Dic312yes—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—22no—
353C2×C3—22no—
354C2×C3—21no—
355C2×C3C2×#87211yescharacteristic
356C2×C3#550411yescharacteristic
357C2×C3#551611yescharacteristic
358C2×C3#556112yes—
359C2×C3#558212yes—
360C2×C3#558312yes—
361C2×C3#558312yes—
362C2×C3C2×#92611yescharacteristic
363C2×C3#581211yescharacteristic
364C2×C3#582711yescharacteristic
365C22#6429712yes—
366C22#6429711yescharacteristic
367C22C2×#379812yes—
368C22#6430711yescharacteristic
369C22C22×D3×Dic311yescharacteristic
370C4—22no—
371C4—22no—
372C4—64no—
373C4—64no—
374C4—124no—
375C4—362no—
376C4—362no—
377C4#6385514yes—
378C3—21no—
379C3#7362511yescharacteristic, complemented
380C3#8245411yescharacteristic, complemented
381C2#1059387612yes—
382C2#1059388312yes—
383C2#1059481811yescharacteristic
384C2C2×#6385511yescharacteristic
385C2#1059498611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2320
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
85. C4×Dic6Dic3semidirect
326. C32#2320semidirect
379. C3#73625semidirect
380. C3#82454semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
#105926312
C3×C4×C4⋊Dic32
#105913572
#105912232
#105912212
#105912062
#105912012
#824543
#736253