Finite Group Databasebeta

← #11805568

Subgroups — #11805568

Order 1152.

1233 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2C2×#63843C212yesmaximal
3C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
4C3×#4935C211yesmaximal, characteristic
5#10591357C212yesmaximal
6#10591349C212yesmaximal
7Dic3×C4⋊Dic3C212yesmaximal
8#10591265C214yesmaximal
9Q8×C4⋊Dic3—31nomaximal
10#74323—31nomaximal
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4×C3⋊Dic3C2212yes—
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4⋊Dic3C2212yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C3×C4×Dic6C418yescomplemented
23C2×Dic3⋊Dic3C2214yes—
24C2×Dic3⋊Dic3C2214yes—
25C2×Dic32C2214yes—
26#63843—28no—
27#63658C2212yes—
28#63579C2214yes—
29C2×C3×C4×Q8—31no—
30C2×Q8×Dic3—32no—
31C2×#887—32no—
32C2×C4×Dic6D311yescharacteristic
33C3×#384—31no—
34#4984—34no—
35#4984—32no—
36#4976—34no—
37#4975—32no—
38Dic3×C4⋊C4—32no—
39#4972—32no—
40#4935—32no—
41#4935D311yescharacteristic
42C4×C4⋊Dic3—31no—
43C4×C4⋊Dic3—31no—
44C4×C4⋊Dic3—32no—
45C4×C4⋊Dic3—61no—
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2312yes—
50C22×C3⋊Dic3C2312yes—
51C22×C3×Dic3C2314yes—
52C22×C3×Dic3C2312yes—
53C22×C3×Dic3C2312yes—
54C2×C3×Dic6C2×C414yes—
55C2×C3×Dic6D414yes—
56C2×C3×Dic6Q814yes—
57C32×C42C2×C414yes—
58C4⋊(C3⋊Dic3)—22no—
59C4⋊(C3⋊Dic3)Q814yescomplemented
60C4×C3⋊Dic3—24no—
61C3×C4⋊Dic3—24no—
62C3×C4⋊Dic3—24no—
63C3×C4⋊Dic3—42no—
64C3×C4⋊Dic3C2×C414yes—
65C3×Dic3⋊C4C2×C418yes—
66C3×C4×Dic3C2×C418yes—
67Dic3⋊Dic3—28no—
68Dic3⋊Dic3—44no—
69Dic32—28no—
70Q8×C4⋊C4—91noSylow
71C22×C3×Q8—31no—
72C22×Dic6C2×D311yescharacteristic
73C3×C4×Q8—38no—
74C2×C3×C4⋊C4—32no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—32no—
77C2×C3×C4⋊C4—32no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C42—21no—
80C2×C3×C42—32no—
81C2×C3×C42C2×D311yescharacteristic
82C2×C3×C42C2×D311yescharacteristic
83Q8×Dic3—68no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—34no—
89C2×C4⋊Dic3—34no—
90C2×C4⋊Dic3—61no—
91C2×C4⋊Dic3—61no—
92C2×C4⋊Dic3C2×D312yes—
93C2×C4⋊Dic3C2×D312yes—
94C2×C4⋊Dic3C2×D312yes—
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×Dic3⋊C4—34no—
97C2×Dic3⋊C4—34no—
98C2×Dic3⋊C4C2×D312yes—
99C2×C4×Dic3—32no—
100C2×C4×Dic3—32no—
101C2×C4×Dic3—34no—
102C2×C4×Dic3—34no—
103C2×C4×Dic3—62no—
104C2×C4×Dic3C2×D312yes—
105#887—68no—
106C4×Dic6Dic318yescomplemented
107C3⋊#95—32no—
108C3⋊#95—32no—
109C3⋊#95—34no—
110C3⋊#95—34no—
111C3⋊#95—62no—
112C23×C32C2411yescharacteristic
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4C22×C412yes—
116C2×C32×C4C22×C412yes—
117C2×C32×C4C22×C412yes—
118C2×C32×C4C2×D412yes—
119C2×C32×C4C2×Q812yes—
120C2×C32×C4C2×Q812yes—
121C2×C32×C4#4112yes—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3C2×Q814yes—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3—24no—
132C2×C3×Dic3—24no—
133C2×C3×Dic3C22×C414yes—
134C2×C3×Dic3C22×C414yes—
135C2×C3×Dic3C2×D414yes—
136C2×C3×Dic3C2×Q814yes—
137C3×Dic6C4⋊C4116yescomplemented
138C2×C4×Q8—31no—
139C2×C4×Q8—92no—
140#389—92no—
141#389—94no—
142#384—31no—
143#384—92no—
144C4×C4⋊C4—92no—
145C4×C4⋊C4—91no—
146C2×C3×Q8—34no—
147C2×C3×Q8—34no—
148C2×C3×Q8—34no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—32no—
153C22×C3×C4—32no—
154C22×C3×C4—34no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×Dic3—32no—
162C22×Dic3—32no—
163C22×Dic3—32no—
164C22×Dic3—32no—
165C22×Dic3—62no—
166C22×Dic3—62no—
167C22×Dic3C22×D314yes—
168C22×Dic3C22×D312yes—
169C22×Dic3C22×D312yes—
170C2×Dic6Dic614yes—
171C2×Dic6D1214yes—
172C2×Dic6C2×Dic314yes—
173C3×C4⋊C4—38no—
174C3×C4⋊C4—34no—
175C3×C4⋊C4—64no—
176C3×C4⋊C4—64no—
177C3×C4⋊C4—122no—
178C3×C42—24no—
179C3×C42—38no—
180C3×C42C4×D314yes—
181C3×C42C2×Dic314yes—
182C4⋊Dic3—24no—
183C4⋊Dic3—24no—
184C4⋊Dic3—34no—
185C4⋊Dic3—34no—
186C4⋊Dic3—42no—
187C4⋊Dic3—64no—
188C4⋊Dic3—68no—
189C4⋊Dic3—64no—
190C4⋊Dic3—62no—
191C4⋊Dic3—62no—
192C4⋊Dic3—124no—
193C4⋊Dic3C2×Dic314yes—
194Dic3⋊C4—68no—
195Dic3⋊C4—124no—
196Dic3⋊C4C2×Dic318yes—
197C4×Dic3—68no—
198C4×Dic3—64no—
199C4×Dic3—64no—
200C4×Dic3—68no—
201C4×Dic3—124no—
202C4×Dic3C2×Dic318yes—
203C22×C32C23×C411yescharacteristic
204C22×C32C22×D411yescharacteristic
205C22×C32C22×Q811yescharacteristic
206C22×C32C22×Q811yescharacteristic
207C22×C32C2×#4111yescharacteristic
208C22×C32H(5,𝔽2)11yescharacteristic
209C22×C322−1+411yescharacteristic
210C32×C4—22no—
211C32×C4C2×C4⋊C414yes—
212C32×C4C4×Q814yescomplemented
213C3⋊Dic3—24no—
214C3⋊Dic3—42no—
215C3×Dic3—24no—
216C3×Dic3—44no—
217C3×Dic3C2×C4⋊C418yes—
218C22×Q8—31no—
219C4×Q8—38no—
220C4×Q8—188no—
221C2×C4⋊C4—32no—
222C2×C4⋊C4—31no—
223C2×C4⋊C4—32no—
224C2×C4⋊C4—32no—
225C2×C4⋊C4—32no—
226C2×C4⋊C4—91no—
227C2×C4⋊C4—94no—
228C2×C4⋊C4—91no—
229C2×C4⋊C4—94no—
230C2×C42—32no—
231C2×C42—94no—
232C2×C42—92no—
233C2×C42D3211yescharacteristic
234#95—94no—
235#95—92no—
236C23×C3—21no—
237C23×C3C23×D311yescharacteristic
238C23×C3C23×D311yescharacteristic
239C3×Q8—316no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—34no—
252C2×C3×C4—34no—
253C2×C3×C4—34no—
254C2×C3×C4—34no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—62no—
258C2×C3×C4—62no—
259C2×C3×C4—64no—
260C2×C3×C4—64no—
261C2×C3×C4—64no—
262C2×C3×C4C2×Dic612yes—
263C2×C3×C4C2×C4×D312yes—
264C2×C3×C4C2×C4×D312yes—
265C2×C3×C4C2×C4×D312yes—
266C2×C3×C4C2×D1212yes—
267C2×C3×C4D3×D412yes—
268C2×C3×C4#23712yes—
269C2×C3×C4D3×Q812yes—
270C2×C3×C4D3×Q812yes—
271C2×C3×C4D3×Q812yes—
272C2×C3×C4#23912yes—
273C2×C3×C4C22×Dic312yes—
274C2×C3×C4C22×Dic312yes—
275C2×C3×C4C22×Dic312yes—
276C2×Dic3—22no—
277C2×Dic3—22no—
278C2×Dic3—24no—
279C2×Dic3—24no—
280C2×Dic3—24no—
281C2×Dic3—34no—
282C2×Dic3—34no—
283C2×Dic3—64no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288C2×Dic3—64no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—62no—
295C2×Dic3—122no—
296C2×Dic3—122no—
297C2×Dic3—122no—
298C2×Dic3—122no—
299C2×Dic3C2×Dic614yes—
300C2×Dic3C2×D1214yes—
301C2×Dic3C22×Dic314yes—
302C2×Dic3C22×Dic314yes—
303Dic6C4⋊Dic3116yescomplemented
304C2×C32C22×C4⋊C411yescharacteristic
305C2×C32C2×C4×Q811yescharacteristic
306C2×C32#52011yescharacteristic
307C2×C32D4×Q811yescharacteristic
308C2×C32#55011yescharacteristic
309C2×C32#55711yescharacteristic
310C2×C32Q8211yescharacteristic
311C2×Q8—34no—
312C2×Q8—34no—
313C2×Q8—34no—
314C22×C4—32no—
315C22×C4—32no—
316C22×C4—34no—
317C22×C4—92no—
318C22×C4—92no—
319C22×C4C2×D3211yescharacteristic
320C22×C4C2×D3211yescharacteristic
321C22×C4C2×D3211yescharacteristic
322C4⋊C4—38no—
323C4⋊C4—34no—
324C4⋊C4—64no—
325C4⋊C4—64no—
326C4⋊C4—94no—
327C4⋊C4—122no—
328C4⋊C4—188no—
329C4⋊C4—182no—
330C4⋊C4—364no—
331C42—38no—
332C42—188no—
333C42—184no—
334C42D3×Dic314yes—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3C22×Dic611yescharacteristic
343C22×C3C22×C4×D311yescharacteristic
344C22×C3C22×D1211yescharacteristic
345C22×C3C2×D3×D411yescharacteristic
346C22×C3C2×#23711yescharacteristic
347C22×C3#100411yescharacteristic
348C22×C3C2×D3×Q811yescharacteristic
349C22×C3C2×D3×Q811yescharacteristic
350C22×C3C2×D3×Q811yescharacteristic
351C22×C3C2×#23911yescharacteristic
352C22×C3#100711yescharacteristic
353C22×C3#100911yescharacteristic
354C22×C3#101011yescharacteristic
355C22×C3C23×Dic311yescharacteristic
356C3×C4—22no—
357C3×C4—22no—
358C3×C4—24no—
359C3×C4—24no—
360C3×C4—38no—
361C3×C4—42no—
362C3×C4—64no—
363C3×C4—124no—
364C3×C4#88714yescomplemented
365C3×C4D3×C4⋊C414yes—
366C3×C4C2×C4⋊Dic314yes—
367C3×C4Q8×Dic314yescomplemented
368Dic3—24no—
369Dic3—44no—
370Dic3—64no—
371Dic3—64no—
372Dic3—124no—
373Dic3—124no—
374Dic3—122no—
375Dic3—122no—
376Dic3C2×C4⋊Dic318yes—
377C32Q8×C4⋊C411yescharacteristic, complemented, Sylow
378C23C22×D3211yescharacteristic
379Q8—316no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—34no—
383C2×C4—34no—
384C2×C4—34no—
385C2×C4—34no—
386C2×C4—62no—
387C2×C4—62no—
388C2×C4—64no—
389C2×C4—64no—
390C2×C4—64no—
391C2×C4—94no—
392C2×C4—182no—
393C2×C4—182no—
394C2×C4—182no—
395C2×C4—182no—
396C2×C4—182no—
397C2×C4D3×Dic612yes—
398C2×C4#379612yes—
399C2×C4#379712yes—
400C2×C4D3×D1212yes—
401C2×C4C2×D3×Dic312yes—
402C2×C4C2×D3×Dic312yes—
403C2×C4C2×D3×Dic312yes—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3C2×#88711yescharacteristic
412C2×C3C2×D3×C4⋊C411yescharacteristic
413C2×C3#550411yescharacteristic
414C2×C3Q8×Dic611yescharacteristic
415C2×C3#557011yescharacteristic
416C2×C3Q8×D1211yescharacteristic
417C2×C3#557711yescharacteristic
418C2×C3#571811yescharacteristic
419C2×C3#572111yescharacteristic
420C2×C3#572211yescharacteristic
421C2×C3#572711yescharacteristic
422C2×C3C22×C4⋊Dic311yescharacteristic
423C2×C3C2×Q8×Dic311yescharacteristic
424C2×C3#582711yescharacteristic
425C22C2×D3×Dic611yescharacteristic
426C22C2×#379611yescharacteristic
427C22#6429711yescharacteristic
428C22C2×#379711yescharacteristic
429C22C2×D3×D1211yescharacteristic
430C22#6430711yescharacteristic
431C22C22×D3×Dic311yescharacteristic
432C4—22no—
433C4—38no—
434C4—64no—
435C4—124no—
436C4—184no—
437C4—362no—
438C4#6384314yescomplemented
439C4D3×C4⋊Dic314yes—
440C3—21no—
441C3#7432311yescharacteristic, complemented
442C3Q8×C4⋊Dic311yescharacteristic, complemented
443C2#1059385611yescharacteristic
444C2#1059386111yescharacteristic
445C2#1059390011yescharacteristic
446C2#1059390311yescharacteristic
447C2C2×#6384311yescharacteristic
448C2C2×D3×C4⋊Dic311yescharacteristic
449C2#1059498611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32Q8×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
22. C3×C4×Dic6C4semidirect
59. C4⋊(C3⋊Dic3)Q8semidirect
106. C4×Dic6Dic3semidirect
137. C3×Dic6C4⋊C4semidirect
212. C32×C4C4×Q8semidirect
303. Dic6C4⋊Dic3semidirect
364. C3×C4#887semidirect
367. C3×C4Q8×Dic3semidirect
377. C32Q8×C4⋊C4semidirect
438. C4#63843semidirect
441. C3#74323semidirect
442. C3Q8×C4⋊Dic3semidirect

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
C4×C4⋊(C3⋊Dic3)2
C3×#49352
#105913572
#105913492
Dic3×C4⋊Dic32
#105912652
Q8×C4⋊Dic33
#743233