Finite Group Databasebeta

← #11803210

Subgroups — #11803210

Order 1152.

985 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
3C3×#4932C211yesmaximal, characteristic
4#10591352C212yesmaximal
5#10591223C212yesmaximal
6#10591220C212yesmaximal
7#10591206C212yesmaximal
8#10591192C214yesmaximal
9#82454—31nomaximal
10#73386—31nomaximal
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2212yes—
14C2×C4×C3⋊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—
22C3×C3⋊#95C2212yes—
23C3×C3⋊#95C2211yescharacteristic
24C3×C3⋊#95C2211yescharacteristic
25#63579C2214yes—
26#63579C2214yes—
27#63579C2214yes—
28C2×C3×C4×Q8—31no—
29C2×C4×Dic6D311yescharacteristic
30C3×#376—31no—
31#5229—32no—
32#4984—32no—
33#4980—34no—
34#4937—32no—
35#4936—32no—
36C4×C4⋊Dic3—31no—
37C4×C4⋊Dic3—31no—
38C4×C4⋊Dic3—61no—
39#4932D311yescharacteristic
40#4929—32no—
41#4928—32no—
42#4652—34no—
43#4651—32no—
44#4650—32no—
45C22×C32×C4C2311yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3C2314yes—
49C22×C3×Dic3C2312yes—
50C22×C3×Dic3C2312yes—
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2312yes—
53C2×C3×Dic6—24no—
54C2×C3×Dic6C2×C414yes—
55C32×C42C2×C414yes—
56C4⋊(C3⋊Dic3)—24no—
57C4×C3⋊Dic3—42no—
58C3×C4⋊Dic3C2×C414yes—
59C3×Dic3⋊C4C2×C418yes—
60C3×C4×Dic3—24no—
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×C42—21no—
70C2×C3×C42—32no—
71C2×C3×C42—32no—
72C2×C3×C42C2×D311yescharacteristic
73C2×C3×C42C2×D311yescharacteristic
74C2×C4⋊Dic3—32no—
75C2×C4⋊Dic3—32no—
76C2×C4⋊Dic3—34no—
77C2×C4⋊Dic3—62no—
78C2×C4⋊Dic3C2×D311yescharacteristic
79C2×Dic3⋊C4—34no—
80C2×Dic3⋊C4C2×D312yes—
81C2×C4×Dic3—32no—
82C2×C4×Dic3—32no—
83C2×C4×Dic3—62no—
84C2×C4×Dic3C2×D312yes—
85C2×C4×Dic3C2×D312yes—
86C4×Dic6Dic318yescomplemented
87C3×#95—31no—
88C3×#95—31no—
89C3×#95—32no—
90C3⋊#95—32no—
91C3⋊#95—32no—
92C3⋊#95—34no—
93C3⋊#95—34no—
94C3⋊#95—34no—
95C3⋊#95—34no—
96C3⋊#95—34no—
97C3⋊#95—34no—
98C3⋊#95—62no—
99C3⋊#95C2×D311yescharacteristic
100C3⋊#95C2×D311yescharacteristic
101C3⋊#95C2×D312yes—
102C23×C32C2411yescharacteristic
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—22no—
106C2×C32×C4C22×C412yes—
107C2×C32×C4C22×C412yes—
108C2×C32×C4C22×C412yes—
109C2×C32×C4#4114yes—
110C2×C3⋊Dic3—24no—
111C2×C3⋊Dic3—24no—
112C2×C3⋊Dic3—24no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—22no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3C22×C414yes—
123C2×C3×Dic3C22×C414yes—
124C3×Dic6—28no—
125C2×C4×Q8—31no—
126#391—92no—
127#389—92no—
128#387—94no—
129#383—92no—
130#382—92no—
131C4×C4⋊C4—91no—
132#376—31no—
133C2×C3×Q8—34no—
134C2×C3×Q8—64no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—32no—
139C22×C3×C4—32no—
140C22×C3×C4—32no—
141C22×C3×C4—32no—
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—34no—
149C22×Dic3—34no—
150C22×Dic3—64no—
151C22×Dic3C22×D312yes—
152C22×Dic3C22×D312yes—
153C22×Dic3C22×D312yes—
154C22×Dic3C22×D312yes—
155C2×Dic6—24no—
156C2×Dic6C2×Dic314yes—
157C3×C4⋊C4—38no—
158C3×C4⋊C4—34no—
159C3×C42—24no—
160C3×C42—38no—
161C3×C42—64no—
162C3×C42C4×D314yes—
163C3×C42C2×Dic314yes—
164C4⋊Dic3—68no—
165C4⋊Dic3—64no—
166C4⋊Dic3—64no—
167C4⋊Dic3—124no—
168C4⋊Dic3C2×Dic314yes—
169Dic3⋊C4—124no—
170Dic3⋊C4C2×Dic318yes—
171C4×Dic3—24no—
172C4×Dic3—122no—
173C4×Dic3—122no—
174C4×Dic3—124no—
175C4×Dic3C2×Dic318yes—
176C22×C32C23×C411yescharacteristic
177C22×C32C2×#4112yes—
178C22×C32H(5,𝔽2)11yescharacteristic
179C22×C322−1+412yes—
180C22×C322−1+411yescharacteristic
181C32×C4—22no—
182C32×C4—22no—
183C32×C4#11714yes—
184C3⋊Dic3—44no—
185C3×Dic3—24no—
186C3×Dic3—24no—
187C3×Dic3—42no—
188C3×Dic3—42no—
189C22×Q8—31no—
190C4×Q8—38no—
191C2×C4⋊C4—32no—
192C2×C4⋊C4—31no—
193C2×C4⋊C4—92no—
194C2×C4⋊C4—94no—
195C2×C42—32no—
196C2×C42—32no—
197C2×C42—92no—
198C2×C42D3211yescharacteristic
199#95—31no—
200#95—31no—
201#95—32no—
202#95—94no—
203#95—94no—
204#95—94no—
205#95—92no—
206C23×C3—21no—
207C23×C3C23×D311yescharacteristic
208C23×C3C23×D311yescharacteristic
209C3×Q8—68no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—22no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—24no—
219C2×C3×C4—22no—
220C2×C3×C4—22no—
221C2×C3×C4—22no—
222C2×C3×C4—34no—
223C2×C3×C4—34no—
224C2×C3×C4—42no—
225C2×C3×C4—64no—
226C2×C3×C4—62no—
227C2×C3×C4—62no—
228C2×C3×C4—62no—
229C2×C3×C4—62no—
230C2×C3×C4—62no—
231C2×C3×C4—62no—
232C2×C3×C4—62no—
233C2×C3×C4—62no—
234C2×C3×C4C2×C4×D312yes—
235C2×C3×C4C2×C4×D312yes—
236C2×C3×C4C2×C4×D312yes—
237C2×C3×C4#23514yes—
238C2×C3×C4#23514yes—
239C2×C3×C4C22×Dic312yes—
240C2×C3×C4C22×Dic312yes—
241C2×C3×C4C22×Dic312yes—
242C2×Dic3—24no—
243C2×Dic3—22no—
244C2×Dic3—22no—
245C2×Dic3—22no—
246C2×Dic3—22no—
247C2×Dic3—22no—
248C2×Dic3—22no—
249C2×Dic3—22no—
250C2×Dic3—22no—
251C2×Dic3—68no—
252C2×Dic3—64no—
253C2×Dic3—64no—
254C2×Dic3—64no—
255C2×Dic3—64no—
256C2×Dic3—64no—
257C2×Dic3—64no—
258C2×Dic3—124no—
259C2×Dic3—124no—
260C2×Dic3C22×Dic314yes—
261C2×Dic3C22×Dic314yes—
262Dic6—28no—
263C2×C32C2×#11711yescharacteristic
264C2×C32#51911yescharacteristic
265C2×C32#52011yescharacteristic
266C2×C32#54112yes—
267C2×C32#54212yes—
268C2×Q8—34no—
269C2×Q8—64no—
270C22×C4—32no—
271C22×C4—32no—
272C22×C4—32no—
273C22×C4—32no—
274C22×C4—94no—
275C22×C4C2×D3211yescharacteristic
276C22×C4C2×D3211yescharacteristic
277C22×C4C2×D3211yescharacteristic
278C4⋊C4—38no—
279C4⋊C4—34no—
280C4⋊C4—184no—
281C4⋊C4—364no—
282C42—38no—
283C42—64no—
284C42—362no—
285C42D3×Dic314yes—
286C22×C3—22no—
287C22×C3—21no—
288C22×C3—22no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3C22×C4×D311yescharacteristic
292C22×C3C2×#23512yes—
293C22×C3C2×#23512yes—
294C22×C3#100712yes—
295C22×C3#100911yescharacteristic
296C22×C3#100911yescharacteristic
297C22×C3#101012yes—
298C22×C3#101011yescharacteristic
299C22×C3#101011yescharacteristic
300C22×C3C23×Dic311yescharacteristic
301C3×C4—24no—
302C3×C4—22no—
303C3×C4—22no—
304C3×C4—22no—
305C3×C4—22no—
306C3×C4—24no—
307C3×C4—42no—
308C3×C4—64no—
309C3×C4—64no—
310C3×C4—122no—
311C3×C4—122no—
312C3×C4#87214yes—
313C3×C4#92614yes—
314Dic3—24no—
315Dic3—24no—
316Dic3—42no—
317Dic3—42no—
318Dic3—128no—
319Dic3—124no—
320Dic3—124no—
321C32#232011yescharacteristic, complemented, Sylow
322C23C22×D3211yescharacteristic
323Q8—68no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—34no—
328C2×C4—34no—
329C2×C4—62no—
330C2×C4—64no—
331C2×C4—62no—
332C2×C4—62no—
333C2×C4—62no—
334C2×C4—62no—
335C2×C4—62no—
336C2×C4—62no—
337C2×C4—62no—
338C2×C4—184no—
339C2×C4—184no—
340C2×C4—184no—
341C2×C4#379814yes—
342C2×C4C2×D3×Dic312yes—
343C2×C4C2×D3×Dic312yes—
344C2×C4C2×D3×Dic312yes—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—22no—
348C2×C3—22no—
349C2×C3—21no—
350C2×C3C2×#87211yescharacteristic
351C2×C3#551611yescharacteristic
352C2×C3#551812yes—
353C2×C3#552311yescharacteristic
354C2×C3#553412yes—
355C2×C3#558212yes—
356C2×C3#558312yes—
357C2×C3C2×#92611yescharacteristic
358C2×C3#581211yescharacteristic
359C2×C3#582711yescharacteristic
360C22#6429712yes—
361C22#6429811yescharacteristic
362C22C2×#379812yes—
363C22#6430811yescharacteristic
364C22C22×D3×Dic311yescharacteristic
365C4—22no—
366C4—22no—
367C4—64no—
368C4—64no—
369C4—122no—
370C4—122no—
371C4—364no—
372C4#6385514yes—
373C3—21no—
374C3#7338611yescharacteristic, complemented
375C3#8245411yescharacteristic, complemented
376C2#1059387812yes—
377C2#1059388012yes—
378C2#1059481811yescharacteristic
379C2C2×#6385511yescharacteristic
380C2#1059499211yescharacteristic
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
86. C4×Dic6Dic3semidirect
321. C32#2320semidirect
374. C3#73386semidirect
375. 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
C4×C4⋊(C3⋊Dic3)2
C3×#49322
#105913522
#105912232
#105912202
#105912062
#105911922
#824543
#733863