Finite Group Databasebeta

← #11801788

Subgroups — #11801788

Order 1152.

1129 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2C42×C3⋊Dic3C211yesmaximal, characteristic
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic
4#10591357C212yesmaximal
5C4×Dic3⋊Dic3C212yesmaximal
6#10591222C212yesmaximal
7#10591221C212yesmaximal
8#10591192C214yesmaximal
9#82451—31nomaximal
10#73618—31nomaximal
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C4×C3⋊Dic3C2212yes—
15C2×C4×C3⋊Dic3C2212yes—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C3×C4×Dic6C418yescomplemented
23C2×Dic3⋊Dic3C2214yes—
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—
36C4×C4⋊Dic3—32no—
37C4×C4⋊Dic3D311yescharacteristic
38#4932—32no—
39#4932—32no—
40C4×Dic3⋊C4—32no—
41C42×Dic3—31no—
42C42×Dic3—31no—
43C42×Dic3—61no—
44#4652—34no—
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—
57C4×C3⋊Dic3—22no—
58C4×C3⋊Dic3—24no—
59C4×C3⋊Dic3Q814yescomplemented
60C3×C4⋊Dic3—24no—
61C3×C4⋊Dic3C2×C414yes—
62C3×Dic3⋊C4C2×C418yes—
63C3×C4×Dic3—24no—
64C3×C4×Dic3C2×C418yes—
65Dic3⋊Dic3—28no—
66#2295—91noSylow
67C22×C3×Q8—31no—
68C22×Dic6C2×D311yescharacteristic
69C3×C4×Q8—38no—
70C2×C3×C4⋊C4—32no—
71C2×C3×C4⋊C4—31no—
72C2×C3×C4⋊C4—32no—
73C2×C3×C42—21no—
74C2×C3×C42—32no—
75C2×C3×C42—32no—
76C2×C3×C42C2×D311yescharacteristic
77C2×C3×C42C2×D311yescharacteristic
78C2×C4⋊Dic3—34no—
79C2×C4⋊Dic3C2×D312yes—
80C2×C4⋊Dic3C2×D311yescharacteristic
81C2×Dic3⋊C4—34no—
82C2×Dic3⋊C4C2×D312yes—
83C2×C4×Dic3—31no—
84C2×C4×Dic3—31no—
85C2×C4×Dic3—32no—
86C2×C4×Dic3—31no—
87C2×C4×Dic3—31no—
88C2×C4×Dic3—32no—
89C2×C4×Dic3—32no—
90C2×C4×Dic3—32no—
91C2×C4×Dic3—61no—
92C2×C4×Dic3—62no—
93C2×C4×Dic3—62no—
94C2×C4×Dic3—61no—
95C2×C4×Dic3C2×D312yes—
96C2×C4×Dic3C2×D312yes—
97C4×Dic6Dic318yescomplemented
98C3×#95—32no—
99C3⋊#95—34no—
100C3⋊#95—34no—
101C3⋊#95—34no—
102C3⋊#95—34no—
103C3⋊#95—34no—
104C3⋊#95—34no—
105C3⋊#95C2×D312yes—
106C23×C32C2411yescharacteristic
107C2×C32×C4—22no—
108C2×C32×C4C22×C412yes—
109C2×C32×C4C22×C412yes—
110C2×C32×C4C22×C412yes—
111C2×C32×C4C2×Q812yes—
112C2×C32×C4#4114yes—
113C2×C32×C4#4112yes—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3C2×Q814yes—
119C2×C3⋊Dic3#4114yes—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—24no—
122C2×C3×Dic3—24no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3C22×C414yes—
126C2×C3×Dic3C22×C414yes—
127C3×Dic6—28no—
128C2×C4×Q8—31no—
129#391—92no—
130#389—92no—
131#387—94no—
132C4×C4⋊C4—31no—
133C4×C4⋊C4—92no—
134#376—92no—
135C43—91no—
136C2×C3×Q8—34no—
137C2×C3×Q8—64no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—32no—
142C22×C3×C4—32no—
143C22×C3×C4—34no—
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C22×C3×C4C22×D311yescharacteristic
147C22×C3×C4C22×D311yescharacteristic
148C22×C3×C4C22×D311yescharacteristic
149C22×C3×C4C22×D311yescharacteristic
150C22×Dic3—32no—
151C22×Dic3—32no—
152C22×Dic3—32no—
153C22×Dic3—32no—
154C22×Dic3—62no—
155C22×Dic3—62no—
156C22×Dic3C22×D314yes—
157C22×Dic3C22×D312yes—
158C22×Dic3C22×D312yes—
159C2×Dic6—24no—
160C2×Dic6C2×Dic314yes—
161C3×C4⋊C4—38no—
162C3×C4⋊C4—34no—
163C3×C4⋊C4—64no—
164C3×C42—24no—
165C3×C42—38no—
166C3×C42—64no—
167C3×C42C4×D314yes—
168C3×C42C2×Dic314yes—
169C4⋊Dic3—24no—
170C4⋊Dic3—68no—
171C4⋊Dic3C2×Dic314yes—
172Dic3⋊C4—68no—
173Dic3⋊C4C2×Dic318yes—
174C4×Dic3—24no—
175C4×Dic3—34no—
176C4×Dic3—34no—
177C4×Dic3—64no—
178C4×Dic3—64no—
179C4×Dic3—64no—
180C4×Dic3—68no—
181C4×Dic3—64no—
182C4×Dic3—68no—
183C4×Dic3—64no—
184C4×Dic3—64no—
185C4×Dic3—62no—
186C4×Dic3—62no—
187C4×Dic3C2×Dic318yes—
188C22×C32C23×C411yescharacteristic
189C22×C32C22×Q811yescharacteristic
190C22×C32C2×#4112yes—
191C22×C32C2×#4111yescharacteristic
192C22×C32C2×#4112yes—
193C32×C4—22no—
194C32×C4#11714yes—
195C32×C4C4×Q814yes—
196C3⋊Dic3—24no—
197C3⋊Dic3—24no—
198C3×Dic3—24no—
199C3×Dic3—24no—
200C3×Dic3—44no—
201C22×Q8—31no—
202C4×Q8—38no—
203C2×C4⋊C4—32no—
204C2×C4⋊C4—31no—
205C2×C4⋊C4—32no—
206C2×C4⋊C4—94no—
207C2×C42—32no—
208C2×C42—32no—
209C2×C42—91no—
210C2×C42—92no—
211C2×C42—92no—
212C2×C42—91no—
213C2×C42D3211yescharacteristic
214#95—32no—
215#95—94no—
216#95—94no—
217#95—94no—
218C23×C3—21no—
219C23×C3C23×D311yescharacteristic
220C23×C3C23×D311yescharacteristic
221C3×Q8—68no—
222C2×C3×C4—24no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—24no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—34no—
232C2×C3×C4—34no—
233C2×C3×C4—64no—
234C2×C3×C4—64no—
235C2×C3×C4—64no—
236C2×C3×C4—64no—
237C2×C3×C4—64no—
238C2×C3×C4C2×C4×D312yes—
239C2×C3×C4C2×C4×D312yes—
240C2×C3×C4C2×C4×D312yes—
241C2×C3×C4#23514yes—
242C2×C3×C4#23514yes—
243C2×C3×C4#23712yes—
244C2×C3×C4D3×Q812yes—
245C2×C3×C4D3×Q812yes—
246C2×C3×C4#23912yes—
247C2×C3×C4C22×Dic312yes—
248C2×C3×C4C22×Dic312yes—
249C2×C3×C4C22×Dic312yes—
250C2×Dic3—24no—
251C2×Dic3—24no—
252C2×Dic3—24no—
253C2×Dic3—24no—
254C2×Dic3—24no—
255C2×Dic3—34no—
256C2×Dic3—34no—
257C2×Dic3—34no—
258C2×Dic3—34no—
259C2×Dic3—64no—
260C2×Dic3—64no—
261C2×Dic3—64no—
262C2×Dic3—64no—
263C2×Dic3—64no—
264C2×Dic3—64no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—62no—
269C2×Dic3—62no—
270C2×Dic3—62no—
271C2×Dic3—62no—
272C2×Dic3—62no—
273C2×Dic3C22×Dic314yes—
274C2×Dic3C22×Dic314yes—
275Dic6—28no—
276C2×C32C2×#11711yescharacteristic
277C2×C32C2×C4×Q811yescharacteristic
278C2×C32C4×#4111yescharacteristic
279C2×C32#52912yes—
280C2×C32#53312yes—
281C2×Q8—34no—
282C2×Q8—64no—
283C22×C4—32no—
284C22×C4—32no—
285C22×C4—34no—
286C22×C4—92no—
287C22×C4—92no—
288C22×C4C2×D3211yescharacteristic
289C22×C4C2×D3211yescharacteristic
290C22×C4C2×D3211yescharacteristic
291C4⋊C4—38no—
292C4⋊C4—34no—
293C4⋊C4—64no—
294C4⋊C4—188no—
295C42—38no—
296C42—64no—
297C42—94no—
298C42—184no—
299C42—182no—
300C42—184no—
301C42D3×Dic314yes—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—21no—
307C22×C3C22×C4×D311yescharacteristic
308C22×C3C2×#23512yes—
309C22×C3C2×#23512yes—
310C22×C3C2×#23711yescharacteristic
311C22×C3C2×D3×Q811yescharacteristic
312C22×C3C2×D3×Q811yescharacteristic
313C22×C3C2×#23911yescharacteristic
314C22×C3D3×#4112yes—
315C22×C3D3×#4112yes—
316C22×C3C23×Dic311yescharacteristic
317C3×C4—24no—
318C3×C4—22no—
319C3×C4—22no—
320C3×C4—24no—
321C3×C4—24no—
322C3×C4—64no—
323C3×C4—64no—
324C3×C4—124no—
325C3×C4#87214yes—
326C3×C4#88714yes—
327C3×C4#92614yes—
328C3×C4Q8×Dic314yes—
329Dic3—24no—
330Dic3—24no—
331Dic3—44no—
332Dic3—68no—
333Dic3—68no—
334Dic3—64no—
335Dic3—64no—
336Dic3—64no—
337Dic3—64no—
338C32#229511yescharacteristic, complemented, Sylow
339C23C22×D3211yescharacteristic
340Q8—68no—
341C2×C4—22no—
342C2×C4—34no—
343C2×C4—34no—
344C2×C4—64no—
345C2×C4—64no—
346C2×C4—64no—
347C2×C4—64no—
348C2×C4—64no—
349C2×C4—94no—
350C2×C4—94no—
351C2×C4—182no—
352C2×C4—182no—
353C2×C4—182no—
354C2×C4—182no—
355C2×C4#379612yes—
356C2×C4#379712yes—
357C2×C4#379814yes—
358C2×C4C2×D3×Dic312yes—
359C2×C4C2×D3×Dic312yes—
360C2×C4C2×D3×Dic312yes—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—22no—
364C2×C3—22no—
365C2×C3—21no—
366C2×C3C2×#87211yescharacteristic
367C2×C3C2×#88711yescharacteristic
368C2×C3#552211yescharacteristic
369C2×C3#555712yes—
370C2×C3#557812yes—
371C2×C3#557812yes—
372C2×C3#558012yes—
373C2×C3C2×#92611yescharacteristic
374C2×C3C2×Q8×Dic311yescharacteristic
375C2×C3Dic3×#4111yescharacteristic
376C22C2×#379611yescharacteristic
377C22C2×#379711yescharacteristic
378C22C2×#379812yes—
379C22#6430612yes—
380C22C22×D3×Dic311yescharacteristic
381C4—22no—
382C4—64no—
383C4—64no—
384C4—124no—
385C4—184no—
386C4—184no—
387C4#6384314yes—
388C4#6385514yes—
389C3—21no—
390C3#7361811yescharacteristic, complemented
391C3#8245111yescharacteristic, complemented
392C2#1059387512yes—
393C2#1059388212yes—
394C2C2×#6384311yescharacteristic
395C2C2×#6385511yescharacteristic
396C2#1059495811yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2295
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
22. C3×C4×Dic6C4semidirect
59. C4×C3⋊Dic3Q8semidirect
97. C4×Dic6Dic3semidirect
338. C32#2295semidirect
390. C3#73618semidirect
391. C3#82451semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
C42×C3⋊Dic32
C3×C4×C4⋊Dic32
#105913572
C4×Dic3⋊Dic32
#105912222
#105912212
#105911922
#824513
#736183