Finite Group Databasebeta

← #11806065

Subgroups — #11806065

Order 1152.

1333 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C3×#4936C211yesmaximal, characteristic, complemented
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
4#10591320C212yesmaximal
5Dic3×C4⋊Dic3C212yesmaximal, complemented
6#10591266C214yesmaximal, complemented
7#10591260C212yesmaximal, complemented
8#10591219C212yesmaximal, complemented
9#74160—31nomaximal
10#73645—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3C2212yes—
13C2×C32×C42C2211yescharacteristic
14C2×#3752C2212yes—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C418yescomplemented
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4⋊Dic3C2212yes—
19C2×C3×C4×Dic3C2212yes—
20C2×#3722C2214yes—
21C2×#3722C2214yes—
22C2×Dic32C2214yes—
23C3×C3⋊#95C2211yescharacteristic
24C3×C3⋊#95C2212yes—
25C3×C3⋊#95C2211yescharacteristic
26C3×C3⋊#95C2212yes—
27#63579C2214yes—
28C2×C4×D12—31no—
29C2×C4×D12—31no—
30C2×C4×D12—61no—
31C3×#382—31no—
32C3×C4×C4⋊C4—31no—
33#4990—34no—
34#4988—32no—
35Dic3×C4⋊C4—32no—
36#4939—32no—
37#4936D311yescharacteristic, complemented
38C4×C4⋊Dic3—32no—
39C4×C4⋊Dic3D311yescharacteristic, complemented
40#4670—34no—
41#4666—32no—
42#4666—32no—
43#4664—32no—
44#4664—32no—
45C23×C3⋊D3C2312yes—
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2312yes—
50C2×C4⋊(C3⋊D3)—22no—
51C2×C4⋊(C3⋊D3)—22no—
52C2×C4⋊(C3⋊D3)C2×C414yes—
53C2×C4×C3⋊D3—44no—
54C2×C4×C3⋊D3C2×C418yes—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2314yes—
57C22×C3×Dic3C2312yes—
58C32×C42C2×C414yes—
59#3752C2×C418yes—
60C4⋊(C3⋊Dic3)C2×C414yes—
61C3×C4⋊Dic3—24no—
62C3×C4⋊Dic3—24no—
63C3×C4×Dic3—24no—
64#3722—28no—
65#3722—44no—
66Dic32—44no—
67#2357—91noSylow
68C22×D12—31no—
69C22×D12—31no—
70C22×D12—61no—
71C22×C4×D3—32no—
72C22×C4×D3—32no—
73C22×C4×D3—62no—
74C2×C3×C4⋊C4—32no—
75C2×C3×C4⋊C4—32no—
76C2×C3×C42—21no—
77C2×C3×C42—32no—
78C2×C3×C42C2×D311yescharacteristic
79C2×C3×C42C2×D311yescharacteristic
80C2×(C2×D3)⋊C4—32no—
81C2×(C2×D3)⋊C4—32no—
82C2×(C2×D3)⋊C4—34no—
83C2×(C2×D3)⋊C4—34no—
84C2×(C2×D3)⋊C4—34no—
85C2×(C2×D3)⋊C4—34no—
86C2×(C2×D3)⋊C4—62no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—61no—
90C2×C4⋊Dic3C2×D312yes—
91C2×C4⋊Dic3C2×D312yes—
92C2×C4×Dic3—34no—
93C2×C4×Dic3—34no—
94C2×C4×Dic3C2×D312yes—
95C4×D12—38no—
96C4×D12—38no—
97C4×D12—68no—
98C3×#95—31no—
99C3×#95—32no—
100C3×#95—31no—
101C3×#95—32no—
102C3⋊#95—34no—
103C3⋊#95—34no—
104C3⋊#95C2×D311yescharacteristic
105C3⋊#95C2×D312yes—
106C3⋊#95C2×D311yescharacteristic
107C3⋊#95C2×D312yes—
108C23×C32C2411yescharacteristic
109C22×C3⋊D3—22no—
110C22×C3⋊D3—22no—
111C22×C3⋊D3—24no—
112C22×C3⋊D3—24no—
113C22×C3⋊D3C22×C414yes—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4C22×C412yes—
117C2×C32×C4C22×C412yes—
118C2×C32×C4C22×C412yes—
119C2×C32×C4#4112yes—
120C2×C32×C4#4112yes—
121C2×C3⋊Dic3—24no—
122C2×C3⋊Dic3C22×C414yes—
123C4⋊(C3⋊D3)—28no—
124C4×C3⋊D3—48no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3—24no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3#4114yes—
134C2×C4×D4—91no—
135#390—92no—
136#388—94no—
137#382—31no—
138#381—92no—
139C4×C4⋊C4—31no—
140C4×C4⋊C4—92no—
141C4×C22⋊C4—92no—
142C23×D3—32no—
143C23×D3—32no—
144C23×D3—62no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—32no—
149C22×C3×C4—32no—
150C22×C3×C4—34no—
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C22×Dic3—32no—
158C22×Dic3—32no—
159C22×Dic3—62no—
160C22×Dic3C22×D312yes—
161C22×Dic3C22×D314yes—
162C22×Dic3C22×D312yes—
163C2×D12—34no—
164C2×D12—34no—
165C2×D12—64no—
166C2×D12—64no—
167C2×D12—64no—
168C2×D12—62no—
169C2×D12—62no—
170C2×D12—62no—
171C2×D12—62no—
172C2×C4×D3—38no—
173C2×C4×D3—38no—
174C2×C4×D3—68no—
175C2×C4×D3—124no—
176C2×C4×D3—124no—
177C2×C4×D3—128no—
178C3×C4⋊C4—64no—
179C3×C4⋊C4—64no—
180C3×C42—24no—
181C3×C42—64no—
182C3×C42C4×D314yes—
183C3×C42C4×D314yes—
184(C2×D3)⋊C4—38no—
185(C2×D3)⋊C4—38no—
186(C2×D3)⋊C4—68no—
187(C2×D3)⋊C4—68no—
188(C2×D3)⋊C4—68no—
189(C2×D3)⋊C4—124no—
190(C2×D3)⋊C4—124no—
191C4⋊Dic3—24no—
192C4⋊Dic3—24no—
193C4⋊Dic3—34no—
194C4⋊Dic3—34no—
195C4⋊Dic3—64no—
196C4×Dic3—24no—
197C4×Dic3—124no—
198C4×Dic3—124no—
199C22×C32C23×C411yescharacteristic
200C22×C32C2×#4112yes—
201C22×C32C2×#4111yescharacteristic
202C22×C32C2×#4111yescharacteristic
203C22×C32H(5,𝔽2)12yes—
204C2×C3⋊D3—24no—
205C2×C3⋊D3—24no—
206C2×C3⋊D3—24no—
207C2×C3⋊D3—44no—
208C2×C3⋊D3—44no—
209C32×C4—22no—
210C32×C4—22no—
211C32×C4#11714yes—
212C3⋊Dic3—24no—
213C3×Dic3—24no—
214C3×Dic3—42no—
215C3×Dic3—44no—
216C22×D4—91no—
217C23×C4—92no—
218C4×D4—98no—
219C2×C4⋊C4—32no—
220C2×C4⋊C4—32no—
221C2×C4⋊C4—91no—
222C2×C22⋊C4—92no—
223C2×C22⋊C4—94no—
224C2×C22⋊C4—94no—
225C2×C42—32no—
226C2×C42—94no—
227C2×C42D3211yescharacteristic
228#95—31no—
229#95—32no—
230#95—31no—
231#95—32no—
232#95—94no—
233C23×C3—21no—
234C23×C3C23×D311yescharacteristic
235C23×C3C23×D311yescharacteristic
236C22×D3—34no—
237C22×D3—34no—
238C22×D3—64no—
239C22×D3—64no—
240C22×D3—64no—
241C22×D3—64no—
242C22×D3—62no—
243C22×D3—62no—
244C22×D3—62no—
245C22×D3—62no—
246C22×D3—64no—
247C22×D3—64no—
248C22×D3—64no—
249C22×D3—124no—
250C22×D3—124no—
251C2×C3×C4—24no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—34no—
262C2×C3×C4—42no—
263C2×C3×C4—62no—
264C2×C3×C4—62no—
265C2×C3×C4—64no—
266C2×C3×C4—62no—
267C2×C3×C4—64no—
268C2×C3×C4—62no—
269C2×C3×C4—64no—
270C2×C3×C4—62no—
271C2×C3×C4C2×C4×D312yes—
272C2×C3×C4C2×C4×D312yes—
273C2×C3×C4C2×C4×D312yes—
274C2×C3×C4C2×C4×D312yes—
275C2×C3×C4C2×C4×D312yes—
276C2×C3×C4C2×C4×D312yes—
277C2×C3×C4#23712yes—
278C2×C3×C4#23712yes—
279C2×C3×C4#23912yes—
280C2×C3×C4#23912yes—
281C2×Dic3—22no—
282C2×Dic3—22no—
283C2×Dic3—22no—
284C2×Dic3—22no—
285C2×Dic3—24no—
286C2×Dic3—24no—
287C2×Dic3—24no—
288C2×Dic3—22no—
289C2×Dic3—34no—
290C2×Dic3—34no—
291C2×Dic3—64no—
292C2×Dic3—64no—
293C2×Dic3—64no—
294C2×Dic3—124no—
295C2×Dic3#23514yes—
296D12—616no—
297D12—68no—
298D12—68no—
299C4×D3—128no—
300C4×D3—128no—
301C4×D3—1216no—
302C2×C32C2×#11711yescharacteristic
303C2×C32C4×#4111yescharacteristic
304C2×C32#51811yescharacteristic
305C2×C32#55312yes—
306C2×C32#55912yes—
307C3⋊D3—44no—
308C24—92no—
309C2×D4—94no—
310C2×D4—182no—
311C2×D4—182no—
312C22×C4—32no—
313C22×C4—34no—
314C22×C4—32no—
315C22×C4—92no—
316C22×C4—98no—
317C22×C4—364no—
318C22×C4C2×D3211yescharacteristic
319C22×C4C2×D3211yescharacteristic
320C22×C4C2×D3211yescharacteristic
321C4⋊C4—64no—
322C4⋊C4—64no—
323C4⋊C4—94no—
324C22⋊C4—98no—
325C22⋊C4—188no—
326C22⋊C4—364no—
327C42—64no—
328C42—364no—
329C42#62414yes—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—21no—
335C22×C3C22×C4×D311yescharacteristic
336C22×C3C22×C4×D311yescharacteristic
337C22×C3C2×#23512yes—
338C22×C3C2×#23711yescharacteristic
339C22×C3C2×#23711yescharacteristic
340C22×C3C2×#23911yescharacteristic
341C22×C3C2×#23911yescharacteristic
342C22×C3D3×#4112yes—
343C22×C3#100912yes—
344C22×C3#100912yes—
345C2×D3—68no—
346C2×D3—64no—
347C2×D3—64no—
348C2×D3—64no—
349C2×D3—64no—
350C2×D3—64no—
351C2×D3—64no—
352C2×D3—124no—
353C2×D3—124no—
354C2×D3—128no—
355C2×D3—128no—
356C2×D3—124no—
357C2×D3—124no—
358C2×D3—124no—
359C2×D3—124no—
360C3×C4—24no—
361C3×C4—22no—
362C3×C4—22no—
363C3×C4—22no—
364C3×C4—22no—
365C3×C4—24no—
366C3×C4—42no—
367C3×C4—64no—
368C3×C4—122no—
369C3×C4—124no—
370C3×C4#89214yes—
371C3×C4#89214yes—
372Dic3—24no—
373Dic3—44no—
374Dic3—42no—
375Dic3—64no—
376Dic3—64no—
377Dic3—124no—
378C32#235711yescharacteristic, complemented, Sylow
379C23—94no—
380C23—182no—
381C23—182no—
382C23—184no—
383C23—184no—
384C23C22×D3211yescharacteristic
385D4—188no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—34no—
389C2×C4—62no—
390C2×C4—62no—
391C2×C4—62no—
392C2×C4—64no—
393C2×C4—64no—
394C2×C4—62no—
395C2×C4—64no—
396C2×C4—62no—
397C2×C4—94no—
398C2×C4—184no—
399C2×C4—368no—
400C2×C4#379612yes—
401C2×C4#379612yes—
402C2×C4C2×#62412yes—
403C2×C4C2×#62412yes—
404C2×C4C2×#62412yes—
405C2×C3—21no—
406C2×C3—22no—
407C2×C3—21no—
408C2×C3—22no—
409C2×C3—21no—
410C2×C3C4×#23511yescharacteristic
411C2×C3C2×#89211yescharacteristic
412C2×C3C2×#89211yescharacteristic
413C2×C3#552111yescharacteristic
414C2×C3#552111yescharacteristic
415C2×C3#552211yescharacteristic
416C2×C3#556512yes—
417C2×C3#558512yes—
418C2×C3#568112yes—
419C2×C3#569512yes—
420D3—128no—
421D3—124no—
422D3—124no—
423C22—184no—
424C22—184no—
425C22—184no—
426C22—364no—
427C22—364no—
428C22C2×#379611yescharacteristic
429C22C2×#379611yescharacteristic
430C22D3×#23512yes—
431C22#6430812yes—
432C22C22×#62411yescharacteristic
433C4—22no—
434C4—22no—
435C4—64no—
436C4—122no—
437C4—124no—
438C4—184no—
439C4#6384914yes—
440C3—21no—
441C3#7364511yescharacteristic, complemented
442C3#7416011yescharacteristic, complemented
443C2—364no—
444C2#1059392512yes—
445C2#1059393912yes—
446C2C2×#6384911yescharacteristic
447C2#1059495411yescharacteristic
448C2#1059499611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32#2357
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4936C2semidirect
3. C3×C4×C4⋊Dic3C2semidirect
5. Dic3×C4⋊Dic3C2semidirect
6. #10591266C2semidirect
7. #10591260C2semidirect
8. #10591219C2semidirect
16. C4×C4⋊(C3⋊D3)C4semidirect
37. #4936D3semidirect
39. C4×C4⋊Dic3D3semidirect
378. C32#2357semidirect
441. C3#73645semidirect
442. C3#74160semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C3×#49362
C3×C4×C4⋊Dic32
#105913202
Dic3×C4⋊Dic32
#105912662
#105912602
#105912192
#741603
#736453