Finite Group Databasebeta

← #11801787

Subgroups — #11801787

Order 1152.

1097 conjugacy classes of subgroups.

The subgroup lattice has 390 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×C42×Dic3C211yesmaximal, characteristic
4#10591352C212yesmaximal
5C4×Dic3⋊Dic3C212yesmaximal
6#10591222C212yesmaximal
7#10591220C212yesmaximal
8#10591201C214yesmaximal
9#82451—31nomaximal
10#73300—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×Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2212yes—
19C2×C3×C4×Dic3C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×C4×Dic3C2211yescharacteristic
22C3×C4×Dic6C418yescomplemented
23C2×Dic3⋊Dic3C2214yes—
24#63658C2212yes—
25#63579C2214yes—
26#63579C2214yes—
27#63579C2214yes—
28C2×C3×C4×Q8—31no—
29C2×C4×Dic6D311yescharacteristic
30C3×C43—31no—
31#5229—32no—
32#4984—32no—
33#4980—34no—
34C4×C4⋊Dic3—31no—
35C4×C4⋊Dic3—31no—
36C4×C4⋊Dic3—32no—
37C4×C4⋊Dic3—61no—
38#4933—34no—
39#4932—32no—
40#4932—32no—
41C4×Dic3⋊C4—32no—
42C42×Dic3D311yescharacteristic
43#4929—32no—
44#4928—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—24no—
58C3×C4⋊Dic3C2×C414yes—
59C3×Dic3⋊C4C2×C418yes—
60C3×C4×Dic3—24no—
61C3×C4×Dic3—22no—
62C3×C4×Dic3—24no—
63C3×C4×Dic3C2×C418yes—
64C3×C4×Dic3Q814yescomplemented
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×C42—21no—
73C2×C3×C42—31no—
74C2×C3×C42—32no—
75C2×C3×C42—32no—
76C2×C3×C42—31no—
77C2×C3×C42—32no—
78C2×C3×C42C2×D311yescharacteristic
79C2×C3×C42C2×D311yescharacteristic
80C2×C4⋊Dic3—32no—
81C2×C4⋊Dic3—32no—
82C2×C4⋊Dic3—34no—
83C2×C4⋊Dic3—62no—
84C2×C4⋊Dic3C2×D311yescharacteristic
85C2×Dic3⋊C4—34no—
86C2×Dic3⋊C4C2×D312yes—
87C2×C4×Dic3—32no—
88C2×C4×Dic3—32no—
89C2×C4×Dic3—62no—
90C2×C4×Dic3C2×D311yescharacteristic
91C2×C4×Dic3C2×D312yes—
92C2×C4×Dic3C2×D312yes—
93C2×C4×Dic3C2×D311yescharacteristic
94C2×C4×Dic3C2×D312yes—
95C4×Dic6Dic318yescomplemented
96C3⋊#95—32no—
97C3⋊#95—32no—
98C3⋊#95—34no—
99C3⋊#95—34no—
100C3⋊#95—34no—
101C3⋊#95—34no—
102C3⋊#95—34no—
103C3⋊#95—34no—
104C3⋊#95—62no—
105C23×C32C2411yescharacteristic
106C2×C32×C4—22no—
107C2×C32×C4C22×C412yes—
108C2×C32×C4C22×C412yes—
109C2×C32×C4C22×C412yes—
110C2×C32×C4C2×Q812yes—
111C2×C32×C4#4114yes—
112C2×C32×C4#4112yes—
113C2×C3⋊Dic3—24no—
114C2×C3⋊Dic3—24no—
115C2×C3⋊Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—22no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—24no—
122C2×C3×Dic3C22×C414yes—
123C2×C3×Dic3C22×C414yes—
124C2×C3×Dic3C2×Q814yes—
125C2×C3×Dic3#4114yes—
126C3×Dic6—28no—
127C2×C4×Q8—31no—
128#391—92no—
129#389—92no—
130#387—94no—
131C4×C4⋊C4—92no—
132C4×C4⋊C4—91no—
133#376—92no—
134C43—31no—
135C2×C3×Q8—34no—
136C2×C3×Q8—64no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—32no—
141C22×C3×C4—32no—
142C22×C3×C4—32no—
143C22×C3×C4—32no—
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—34no—
151C22×Dic3—34no—
152C22×Dic3—64no—
153C22×Dic3C22×D312yes—
154C22×Dic3C22×D312yes—
155C22×Dic3C22×D312yes—
156C22×Dic3C22×D312yes—
157C2×Dic6—24no—
158C2×Dic6C2×Dic314yes—
159C3×C4⋊C4—38no—
160C3×C4⋊C4—34no—
161C3×C42—24no—
162C3×C42—38no—
163C3×C42—34no—
164C3×C42—64no—
165C3×C42—64no—
166C3×C42—62no—
167C3×C42C4×D314yes—
168C3×C42C2×Dic314yes—
169C4⋊Dic3—68no—
170C4⋊Dic3—64no—
171C4⋊Dic3—64no—
172C4⋊Dic3—68no—
173C4⋊Dic3C2×Dic314yes—
174Dic3⋊C4—68no—
175Dic3⋊C4C2×Dic318yes—
176C4×Dic3—24no—
177C4×Dic3—22no—
178C4×Dic3—24no—
179C4×Dic3—64no—
180C4×Dic3—64no—
181C4×Dic3—124no—
182C4×Dic3Dic614yescomplemented
183C4×Dic3C2×Dic318yes—
184C22×C32C23×C411yescharacteristic
185C22×C32C22×Q811yescharacteristic
186C22×C32C2×#4112yes—
187C22×C32C2×#4111yescharacteristic
188C22×C32C2×#4112yes—
189C32×C4—22no—
190C32×C4#11714yes—
191C32×C4C4×Q814yes—
192C3⋊Dic3—44no—
193C3×Dic3—24no—
194C3×Dic3—24no—
195C3×Dic3—24no—
196C3×Dic3—24no—
197C22×Q8—31no—
198C4×Q8—38no—
199C2×C4⋊C4—32no—
200C2×C4⋊C4—31no—
201C2×C4⋊C4—94no—
202C2×C4⋊C4—92no—
203C2×C42—32no—
204C2×C42—31no—
205C2×C42—32no—
206C2×C42—32no—
207C2×C42—31no—
208C2×C42—92no—
209C2×C42D3211yescharacteristic
210#95—94no—
211#95—94no—
212#95—94no—
213#95—92no—
214C23×C3—21no—
215C23×C3C23×D311yescharacteristic
216C23×C3C23×D311yescharacteristic
217C3×Q8—68no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—22no—
221C2×C3×C4—24no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—34no—
227C2×C3×C4—34no—
228C2×C3×C4—34no—
229C2×C3×C4—34no—
230C2×C3×C4—42no—
231C2×C3×C4—64no—
232C2×C3×C4—62no—
233C2×C3×C4—62no—
234C2×C3×C4—64no—
235C2×C3×C4—62no—
236C2×C3×C4—62no—
237C2×C3×C4C2×Dic612yes—
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#23512yes—
244C2×C3×C4D3×Q812yes—
245C2×C3×C4#23912yes—
246C2×C3×C4C22×Dic312yes—
247C2×C3×C4C22×Dic312yes—
248C2×C3×C4C22×Dic312yes—
249C2×Dic3—22no—
250C2×Dic3—22no—
251C2×Dic3—22no—
252C2×Dic3—22no—
253C2×Dic3—24no—
254C2×Dic3—24no—
255C2×Dic3—68no—
256C2×Dic3—64no—
257C2×Dic3—64no—
258C2×Dic3—64no—
259C2×Dic3—64no—
260C2×Dic3—64no—
261C2×Dic3—64no—
262C2×Dic3—124no—
263C2×Dic3—124no—
264C2×Dic3C2×Dic614yes—
265C2×Dic3#23514yes—
266C2×Dic3C22×Dic314yes—
267C2×Dic3C22×Dic314yes—
268Dic6—28no—
269C2×C32C2×#11711yescharacteristic
270C2×C32C2×C4×Q811yescharacteristic
271C2×C32C4×#4111yescharacteristic
272C2×C32#52912yes—
273C2×C32#53312yes—
274C2×Q8—34no—
275C2×Q8—64no—
276C22×C4—32no—
277C22×C4—32no—
278C22×C4—32no—
279C22×C4—32no—
280C22×C4—94no—
281C22×C4C2×D3211yescharacteristic
282C22×C4C2×D3211yescharacteristic
283C22×C4C2×D3211yescharacteristic
284C4⋊C4—38no—
285C4⋊C4—34no—
286C4⋊C4—188no—
287C4⋊C4—184no—
288C42—34no—
289C42—38no—
290C42—64no—
291C42—64no—
292C42—62no—
293C42—184no—
294C42D3×Dic314yes—
295C22×C3—21no—
296C22×C3—22no—
297C22×C3—21no—
298C22×C3—22no—
299C22×C3—21no—
300C22×C3C22×Dic611yescharacteristic
301C22×C3C22×C4×D311yescharacteristic
302C22×C3C2×#23512yes—
303C22×C3C2×#23512yes—
304C22×C3C2×#23511yescharacteristic
305C22×C3C2×#23512yes—
306C22×C3C2×D3×Q811yescharacteristic
307C22×C3C2×#23911yescharacteristic
308C22×C3D3×#4112yes—
309C22×C3C23×Dic311yescharacteristic
310C3×C4—22no—
311C3×C4—22no—
312C3×C4—24no—
313C3×C4—24no—
314C3×C4—42no—
315C3×C4—64no—
316C3×C4—64no—
317C3×C4—64no—
318C3×C4—64no—
319C3×C4C4×Dic614yes—
320C3×C4#87214yes—
321C3×C4#92614yes—
322C3×C4Q8×Dic314yes—
323Dic3—24no—
324Dic3—24no—
325Dic3—24no—
326Dic3—24no—
327Dic3—128no—
328Dic3—124no—
329Dic3—124no—
330C32#229511yescharacteristic, complemented, Sylow
331C23C22×D3211yescharacteristic
332Q8—68no—
333C2×C4—22no—
334C2×C4—34no—
335C2×C4—34no—
336C2×C4—34no—
337C2×C4—34no—
338C2×C4—62no—
339C2×C4—62no—
340C2×C4—64no—
341C2×C4—62no—
342C2×C4—62no—
343C2×C4—64no—
344C2×C4—184no—
345C2×C4—184no—
346C2×C4—184no—
347C2×C4D3×Dic612yes—
348C2×C4#379814yes—
349C2×C4#379912yes—
350C2×C4C2×D3×Dic312yes—
351C2×C4C2×D3×Dic312yes—
352C2×C4C2×D3×Dic312yes—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—22no—
356C2×C3—22no—
357C2×C3—21no—
358C2×C3C2×C4×Dic611yescharacteristic
359C2×C3#547012yes—
360C2×C3C2×#87211yescharacteristic
361C2×C3C4×#23511yescharacteristic
362C2×C3#547912yes—
363C2×C3#557812yes—
364C2×C3#558012yes—
365C2×C3C2×#92611yescharacteristic
366C2×C3C2×Q8×Dic311yescharacteristic
367C2×C3Dic3×#4111yescharacteristic
368C22C2×D3×Dic611yescharacteristic
369C22C2×#379812yes—
370C22C2×#379911yescharacteristic
371C22D3×#23512yes—
372C22C22×D3×Dic311yescharacteristic
373C4—22no—
374C4—64no—
375C4—64no—
376C4—64no—
377C4—64no—
378C4—364no—
379C4Dic3×Dic614yes—
380C4#6385514yes—
381C3—21no—
382C3#7330011yescharacteristic, complemented
383C3#8245111yescharacteristic, complemented
384C2#1059387012yes—
385C2#1059387312yes—
386C2C2×Dic3×Dic611yescharacteristic
387C2C2×#6385511yescharacteristic
388C2Dic3×#23511yescharacteristic
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
64. C3×C4×Dic3Q8semidirect
95. C4×Dic6Dic3semidirect
182. C4×Dic3Dic6semidirect
330. C32#2295semidirect
382. C3#73300semidirect
383. 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
C4×C4⋊(C3⋊Dic3)2
C3×C42×Dic32
#105913522
C4×Dic3⋊Dic32
#105912222
#105912202
#105912012
#824513
#733003