Finite Group Databasebeta

← #11800944

Subgroups — #11800944

Order 1152.

1345 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2C2×#63843C212yesmaximal
3#10592631C211yesmaximal, characteristic
4C3×C4×C4⋊Dic3C211yesmaximal, characteristic
5#10591274C212yesmaximal
6#10591242C212yesmaximal
7Dic3×Dic3⋊C4C214yesmaximal
8#10591239C212yesmaximal
9#82450—31nomaximal
10#73616—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—
21C2×Dic32C2214yes—
22C2×Dic32C2214yes—
23#63843C4116yescomplemented
24#63658C2211yescharacteristic
25#63658C2212yes—
26#63658C2211yescharacteristic
27C3×C3⋊#95C2212yes—
28#63579C2214yes—
29C2×C3×C4×Q8—31no—
30C2×Q8×Dic3—32no—
31C2×#887—32no—
32C2×C4×Dic6D311yescharacteristic
33C3×C4×C4⋊C4—31no—
34Dic3×C4⋊C4—32no—
35Dic3×C4⋊C4—32no—
36Dic3×C4⋊C4—34no—
37C4×C4⋊Dic3—32no—
38C4×C4⋊Dic3D311yescharacteristic
39#4932—31no—
40#4932—31no—
41#4932—32no—
42#4932—61no—
43C4×Dic3⋊C4—34no—
44#4649—32no—
45#4648—32no—
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2312yes—
50C22×C3⋊Dic3C2312yes—
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2314yes—
53C22×C3×Dic3C2312yes—
54C2×C3×Dic6C2×C418yes—
55C2×C3×Dic6C2×C414yes—
56C32×C42C2×C414yes—
57C4×C3⋊Dic3C2×C418yes—
58C3×C4⋊Dic3C2×C418yes—
59C3×C4⋊Dic3C2×C414yes—
60C3×Dic3⋊C4C2×C418yes—
61C3×C4×Dic3—42no—
62C3×C4×Dic3C2×C418yes—
63Dic3⋊Dic3C2×C4116yes—
64Dic32—44no—
65Dic32C2×C4116yes—
66#2276—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
78Q8×Dic3—316no—
79C2×C4⋊Dic3—34no—
80C2×C4⋊Dic3C2×D312yes—
81C2×C4⋊Dic3C2×D311yescharacteristic
82C2×Dic3⋊C4—34no—
83C2×Dic3⋊C4C2×D312yes—
84C2×C4×Dic3—32no—
85C2×C4×Dic3—32no—
86C2×C4×Dic3—34no—
87C2×C4×Dic3—34no—
88C2×C4×Dic3—34no—
89C2×C4×Dic3—34no—
90C2×C4×Dic3—62no—
91C2×C4×Dic3C2×D312yes—
92C2×C4×Dic3C2×D312yes—
93#887—316no—
94C4×Dic6Dic318yescomplemented
95C3×#95—32no—
96C3⋊#95—31no—
97C3⋊#95—31no—
98C3⋊#95—32no—
99C3⋊#95—31no—
100C3⋊#95—31no—
101C3⋊#95—32no—
102C3⋊#95—34no—
103C3⋊#95—34no—
104C3⋊#95—61no—
105C3⋊#95—62no—
106C3⋊#95—61no—
107C3⋊#95C2×D312yes—
108C23×C32C2411yescharacteristic
109C2×C32×C4—21no—
110C2×C32×C4—22no—
111C2×C32×C4—21no—
112C2×C32×C4C22×C414yes—
113C2×C32×C4C22×C412yes—
114C2×C32×C4C22×C412yes—
115C2×C32×C4C22×C412yes—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3C22×C414yes—
121C2×C3⋊Dic3C22×C414yes—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3C22×C418yes—
127C2×C3×Dic3C22×C418yes—
128C2×C3×Dic3C22×C414yes—
129C2×C3×Dic3C22×C414yes—
130C3×Dic6C42116yescomplemented
131C2×C4×Q8—31no—
132C2×C4×Q8—92no—
133C4×C4⋊C4—31no—
134C4×C4⋊C4—92no—
135C4×C4⋊C4—94no—
136C4×C4⋊C4—92no—
137#376—92no—
138#376—91no—
139C2×C3×Q8—38no—
140C2×C3×Q8—34no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—32no—
145C22×C3×C4—32no—
146C22×C3×C4—34no—
147C22×C3×C4C22×D311yescharacteristic
148C22×C3×C4C22×D311yescharacteristic
149C22×C3×C4C22×D311yescharacteristic
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C22×Dic3—32no—
154C22×Dic3—32no—
155C22×Dic3—32no—
156C22×Dic3—32no—
157C22×Dic3—62no—
158C22×Dic3—62no—
159C22×Dic3C22×D314yes—
160C22×Dic3C22×D312yes—
161C22×Dic3C22×D312yes—
162C2×Dic6C4×D318yes—
163C2×Dic6C2×Dic314yes—
164C3×C4⋊C4—38no—
165C3×C4⋊C4—38no—
166C3×C4⋊C4—34no—
167C3×C42—24no—
168C3×C42—38no—
169C3×C42—122no—
170C3×C42C4×D314yes—
171C3×C42C2×Dic314yes—
172C4⋊Dic3—316no—
173C4⋊Dic3C4×D318yes—
174C4⋊Dic3C2×Dic314yes—
175Dic3⋊C4—316no—
176Dic3⋊C4C2×Dic318yes—
177C4×Dic3—38no—
178C4×Dic3—38no—
179C4×Dic3—316no—
180C4×Dic3—316no—
181C4×Dic3—42no—
182C4×Dic3—68no—
183C4×Dic3—124no—
184C4×Dic3—124no—
185C4×Dic3C2×Dic318yes—
186C22×C32C23×C412yes—
187C22×C32C23×C411yescharacteristic
188C22×C32H(5,𝔽2)11yescharacteristic
189C22×C322−1+411yescharacteristic
190C22×C322−1+412yes—
191C32×C4—22no—
192C32×C4—22no—
193C32×C4C2×C4214yes—
194C3⋊Dic3—24no—
195C3⋊Dic3—24no—
196C3×Dic3—28no—
197C3×Dic3—24no—
198C3×Dic3C2×C4218yes—
199C22×Q8—31no—
200C4×Q8—38no—
201C4×Q8—916no—
202C2×C4⋊C4—32no—
203C2×C4⋊C4—31no—
204C2×C4⋊C4—32no—
205C2×C4⋊C4—94no—
206C2×C42—32no—
207C2×C42—32no—
208C2×C42—94no—
209C2×C42—92no—
210C2×C42—94no—
211C2×C42D3211yescharacteristic
212#95—32no—
213#95—94no—
214#95—91no—
215#95—92no—
216#95—91no—
217C23×C3—21no—
218C23×C3C23×D311yescharacteristic
219C23×C3C23×D311yescharacteristic
220C3×Q8—316no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—22no—
224C2×C3×C4—21no—
225C2×C3×C4—22no—
226C2×C3×C4—21no—
227C2×C3×C4—24no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—38no—
232C2×C3×C4—34no—
233C2×C3×C4—38no—
234C2×C3×C4—34no—
235C2×C3×C4—42no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—62no—
239C2×C3×C4—62no—
240C2×C3×C4—64no—
241C2×C3×C4—64no—
242C2×C3×C4C2×C4×D314yes—
243C2×C3×C4C2×C4×D314yes—
244C2×C3×C4C2×C4×D312yes—
245C2×C3×C4C2×C4×D312yes—
246C2×C3×C4C2×C4×D312yes—
247C2×C3×C4C22×Dic312yes—
248C2×C3×C4C22×Dic312yes—
249C2×C3×C4C22×Dic312yes—
250C2×Dic3—24no—
251C2×Dic3—22no—
252C2×Dic3—24no—
253C2×Dic3—22no—
254C2×Dic3—34no—
255C2×Dic3—34no—
256C2×Dic3—34no—
257C2×Dic3—34no—
258C2×Dic3—64no—
259C2×Dic3—64no—
260C2×Dic3—62no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—122no—
269C2×Dic3—122no—
270C2×Dic3—122no—
271C2×Dic3—122no—
272C2×Dic3C2×C4×D318yes—
273C2×Dic3C2×C4×D318yes—
274C2×Dic3C22×Dic314yes—
275C2×Dic3C22×Dic314yes—
276Dic6C4×Dic3116yescomplemented
277C2×C32C22×C4211yescharacteristic
278C2×C32#51911yescharacteristic
279C2×C32#51912yes—
280C2×C32#52011yescharacteristic
281C2×C32#52012yes—
282C2×Q8—38no—
283C2×Q8—34no—
284C22×C4—32no—
285C22×C4—34no—
286C22×C4—32no—
287C22×C4—92no—
288C22×C4—92no—
289C22×C4C2×D3211yescharacteristic
290C22×C4C2×D3211yescharacteristic
291C22×C4C2×D3211yescharacteristic
292C4⋊C4—38no—
293C4⋊C4—38no—
294C4⋊C4—34no—
295C4⋊C4—916no—
296C42—38no—
297C42—916no—
298C42—98no—
299C42—122no—
300C42—364no—
301C42D3×Dic314yes—
302C22×C3—22no—
303C22×C3—21no—
304C22×C3—22no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3C22×C4×D312yes—
308C22×C3C22×C4×D312yes—
309C22×C3C22×C4×D311yescharacteristic
310C22×C3#100411yescharacteristic
311C22×C3#100711yescharacteristic
312C22×C3#100712yes—
313C22×C3#100911yescharacteristic
314C22×C3#101012yes—
315C22×C3#101011yescharacteristic
316C22×C3C23×Dic311yescharacteristic
317C3×C4—22no—
318C3×C4—22no—
319C3×C4—22no—
320C3×C4—22no—
321C3×C4—24no—
322C3×C4—38no—
323C3×C4—42no—
324C3×C4—42no—
325C3×C4—64no—
326C3×C4—68no—
327C3×C4C42×D314yes—
328C3×C4C2×C4×Dic314yes—
329Dic3—28no—
330Dic3—24no—
331Dic3—64no—
332Dic3—64no—
333Dic3—64no—
334Dic3—64no—
335Dic3—124no—
336Dic3—124no—
337Dic3C2×C4×Dic318yes—
338C32#227611yescharacteristic, complemented, Sylow
339C23C22×D3211yescharacteristic
340Q8—316no—
341C2×C4—22no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—38no—
345C2×C4—34no—
346C2×C4—38no—
347C2×C4—34no—
348C2×C4—64no—
349C2×C4—62no—
350C2×C4—64no—
351C2×C4—62no—
352C2×C4—94no—
353C2×C4—94no—
354C2×C4—182no—
355C2×C4—182no—
356C2×C4—182no—
357C2×C4—182no—
358C2×C4C4×D3214yes—
359C2×C4C2×D3×Dic312yes—
360C2×C4C2×D3×Dic312yes—
361C2×C4C2×D3×Dic312yes—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—22no—
365C2×C3—22no—
366C2×C3—21no—
367C2×C3C2×C42×D311yescharacteristic
368C2×C3#550411yescharacteristic
369C2×C3#551611yescharacteristic
370C2×C3#554612yes—
371C2×C3#557212yes—
372C2×C3#557212yes—
373C2×C3#557412yes—
374C2×C3C22×C4×Dic311yescharacteristic
375C2×C3#581211yescharacteristic
376C2×C3#582711yescharacteristic
377C22#6429712yes—
378C22#6429711yescharacteristic
379C22C2×C4×D3212yes—
380C22#6430711yescharacteristic
381C22C22×D3×Dic311yescharacteristic
382C4—22no—
383C4—22no—
384C4—38no—
385C4—68no—
386C4—64no—
387C4—184no—
388C4—184no—
389C4C4×D3×Dic314yes—
390C3—21no—
391C3#7361611yescharacteristic, complemented
392C3#8245011yescharacteristic, complemented
393C2#1059384812yes—
394C2#1059388912yes—
395C2#1059481811yescharacteristic
396C2C2×C4×D3×Dic311yescharacteristic
397C2#1059498611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2276
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
19. C3×C4×Dic6C4semidirect
23. #63843C4semidirect
94. C4×Dic6Dic3semidirect
130. C3×Dic6C42semidirect
276. Dic6C4×Dic3semidirect
338. C32#2276semidirect
391. C3#73616semidirect
392. C3#82450semidirect

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×#638432
#105926312
C3×C4×C4⋊Dic32
#105912742
#105912422
Dic3×Dic3⋊C42
#105912392
#824503
#736163