Finite Group Databasebeta

← #11801956

Subgroups — #11801956

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63855C211yesmaximal, characteristic
2#10592631C211yesmaximal, characteristic, complemented
3C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
4C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6#10591285C212yesmaximal
7#10591284C212yesmaximal
8C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic
9#10591254C212yesmaximal, complemented
10#10591253C212yesmaximal, complemented
11C4×Dic32C211yesmaximal, characteristic, complemented
12#73620—31nomaximal
13#73440—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×Dic3⋊Dic3C2212yes—
24C2×Dic3⋊Dic3C2211yescharacteristic
25C2×Dic3⋊Dic3C2211yescharacteristic
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2211yescharacteristic
28C2×(C2×D3)⋊Dic3C2211yescharacteristic
29C2×Dic32C2212yes—
30C2×Dic32C2212yes—
31#63855C418yescomplemented
32#63658C2212yes—
33#63658C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×#926—31no—
39C2×#872—31no—
40C3×C4×C4⋊C4—31no—
41C3×C4×C22⋊C4—31no—
42C4×#217—31no—
43#4990—32no—
44#4978—32no—
45#4945—32no—
46#4944—32no—
47C4×(C2×D3)⋊C4—31no—
48C4×(C2×D3)⋊C4D311yescharacteristic
49C4×C4⋊Dic3—31no—
50#4932—31no—
51#4932—31no—
52#4932—61no—
53C4×Dic3⋊C4—31no—
54C4×Dic3⋊C4D311yescharacteristic, complemented
55C42×Dic3—31no—
56C42×Dic3—31no—
57#4670—32no—
58#4655—32no—
59#4654—32no—
60#4653—32no—
61C23×C3×D3C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3C2312yes—
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3×Dic3C2311yescharacteristic
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3C2×C414yes—
75C32×C42—22no—
76C4×C3⋊Dic3—22no—
77C4×C3⋊Dic3C2×C414yes—
78C3×(C2×D3)⋊C4—24no—
79C3×Dic3⋊C4—24no—
80C3×C4×Dic3—22no—
81C3×C4×Dic3—22no—
82C3×C4×Dic3C2×C414yes—
83Dic3⋊Dic3—24no—
84Dic3⋊Dic3C2×C414yes—
85Dic3⋊Dic3C2×C414yes—
86(C2×D3)⋊Dic3—24no—
87(C2×D3)⋊Dic3C2×C414yes—
88(C2×D3)⋊Dic3C2×C414yes—
89Dic32—24no—
90Dic32—24no—
91#2298—91noSylow
92C23×C3×C4—31no—
93C22×C4×D3C2×D311yescharacteristic
94C2×C3×C4⋊C4—32no—
95C2×C3×C22⋊C4—32no—
96C2×C3×C42—21no—
97C2×C3×C42—31no—
98C2×C3×C42—31no—
99C2×C3×C42—31no—
100C2×C3×C42C2×D311yescharacteristic
101C2×C3×C42C2×D311yescharacteristic
102C2×#217—31no—
103C2×#217—31no—
104C2×#217—32no—
105C2×(C2×D3)⋊C4—31no—
106C2×(C2×D3)⋊C4—31no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4C2×D312yes—
109#926—38no—
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—32no—
113C2×Dic3⋊C4—31no—
114C2×Dic3⋊C4—31no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4C2×D312yes—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—31no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—61no—
126C2×C4×Dic3—61no—
127C2×C4×Dic3C2×D311yescharacteristic
128C2×C4×Dic3C2×D311yescharacteristic
129C2×C4×Dic3C2×D311yescharacteristic
130#872—38no—
131C3×#95—32no—
132C3×#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—62no—
142C3⋊#95—62no—
143C3⋊#95C2×D312yes—
144C3⋊#95C2×D312yes—
145C23×C32C2411yescharacteristic
146C22×C3×D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3—21no—
149C22×C3×D3—21no—
150C22×C3×D3C22×C412yes—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4C22×C412yes—
155C2×C32×C4#4112yes—
156C2×C32×C4#4112yes—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3C22×C412yes—
163C2×C3⋊Dic3C22×C412yes—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3C22×C412yes—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3#4114yes—
176C2×C3×Dic3#4114yes—
177C3×C4×D3—28no—
178C2×#117—91no—
179#388—92no—
180#388—92no—
181#387—92no—
182#387—92no—
183C4×C4⋊C4—31no—
184C4×C4⋊C4—91no—
185C4×C22⋊C4—31no—
186C4×C22⋊C4—91no—
187#376—91no—
188C43—91no—
189C24×C3—31no—
190C23×D3C22×D311yescharacteristic
191C22×C3×C4—22no—
192C22×C3×C4—21no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—32no—
196C22×C3×C4—32no—
197C22×C3×C4—31no—
198C22×C3×C4—34no—
199C22×C3×C4—62no—
200C22×C3×C4—62no—
201C22×C3×C4C22×D312yes—
202C22×C3×C4C22×D312yes—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×Dic3—31no—
206C22×Dic3—31no—
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—32no—
210C22×Dic3—32no—
211C22×Dic3—61no—
212C22×Dic3—61no—
213C22×Dic3—62no—
214C22×Dic3C22×D311yescharacteristic
215C22×Dic3C22×D311yescharacteristic
216C22×Dic3C22×D311yescharacteristic
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D312yes—
219C2×C4×D3—22no—
220C2×C4×D3—22no—
221C2×C4×D3C4×D314yes—
222C3×C4⋊C4—64no—
223C3×C22⋊C4—64no—
224C3×C42—24no—
225C3×C42—22no—
226C3×C42—22no—
227C3×C42—34no—
228C3×C42—62no—
229C3×C42—62no—
230#217—34no—
231#217—34no—
232#217—64no—
233(C2×D3)⋊C4—24no—
234(C2×D3)⋊C4—34no—
235(C2×D3)⋊C4—34no—
236(C2×D3)⋊C4—64no—
237C4⋊Dic3—34no—
238C4⋊Dic3—34no—
239C4⋊Dic3—64no—
240Dic3⋊C4—24no—
241Dic3⋊C4—34no—
242Dic3⋊C4—34no—
243Dic3⋊C4—64no—
244C4×Dic3—22no—
245C4×Dic3—22no—
246C4×Dic3—34no—
247C4×Dic3—34no—
248C4×Dic3—64no—
249C4×Dic3—64no—
250C4×Dic3—64no—
251C4×Dic3—64no—
252C4×Dic3—62no—
253C4×Dic3—62no—
254C4×Dic3—64no—
255C4×Dic3—64no—
256C4×Dic3C4×D314yes—
257C22×C32C23×C411yescharacteristic
258C22×C32C2×#4112yes—
259C22×C32C2×#4112yes—
260C22×C32C2×#4111yescharacteristic
261C22×C32C2×#4111yescharacteristic
262C2×C3×D3—22no—
263C2×C3×D3—22no—
264C2×C3×D3—22no—
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C32×C4—42no—
268C32×C4#11714yes—
269C3⋊Dic3—22no—
270C3⋊Dic3—22no—
271C3⋊Dic3—42no—
272C3×Dic3—22no—
273C3×Dic3—22no—
274C3×Dic3—22no—
275C3×Dic3—24no—
276C3×Dic3—24no—
277C23×C4—31no—
278#117—98no—
279C2×C4⋊C4—32no—
280C2×C4⋊C4—91no—
281C2×C4⋊C4—91no—
282C2×C4⋊C4—92no—
283C2×C22⋊C4—32no—
284C2×C22⋊C4—91no—
285C2×C22⋊C4—91no—
286C2×C22⋊C4—92no—
287C2×C42—31no—
288C2×C42—31no—
289C2×C42—31no—
290C2×C42—91no—
291C2×C42—92no—
292C2×C42—92no—
293C2×C42—91no—
294C2×C42D3211yescharacteristic
295#95—32no—
296#95—32no—
297#95—92no—
298#95—92no—
299#95—92no—
300#95—92no—
301C23×C3—21no—
302C23×C3—32no—
303C23×C3—62no—
304C23×C3—61no—
305C23×C3—61no—
306C23×C3—62no—
307C23×C3C23×D311yescharacteristic
308C23×C3C23×D311yescharacteristic
309C22×D3—22no—
310C22×D3—21no—
311C22×D3—21no—
312C22×D3—22no—
313C22×D3C2×C4×D312yes—
314C2×C3×C4—24no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—32no—
325C2×C3×C4—32no—
326C2×C3×C4—32no—
327C2×C3×C4—34no—
328C2×C3×C4—34no—
329C2×C3×C4—42no—
330C2×C3×C4—42no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—61no—
336C2×C3×C4—62no—
337C2×C3×C4—61no—
338C2×C3×C4—62no—
339C2×C3×C4—68no—
340C2×C3×C4C2×C4×D312yes—
341C2×C3×C4C2×C4×D312yes—
342C2×C3×C4#23712yes—
343C2×C3×C4#23712yes—
344C2×C3×C4#23712yes—
345C2×C3×C4#23912yes—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—32no—
357C2×Dic3—32no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—64no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373C2×Dic3—122no—
374C2×Dic3—122no—
375C2×Dic3C2×C4×D312yes—
376C2×Dic3C2×C4×D312yes—
377C2×Dic3C2×C4×D312yes—
378C2×Dic3#23514yes—
379C2×Dic3#23514yes—
380C4×D3—28no—
381C2×C32C2×#11711yescharacteristic
382C2×C32C4×#4111yescharacteristic
383C2×C32C4×#4111yescharacteristic
384C2×C32#52912yes—
385C2×C32#52912yes—
386C3×D3—42no—
387C24—31no—
388C22×C4—31no—
389C22×C4—31no—
390C22×C4—32no—
391C22×C4—32no—
392C22×C4—31no—
393C22×C4—34no—
394C22×C4—62no—
395C22×C4—62no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—92no—
399C22×C4C2×D3212yes—
400C22×C4C2×D3211yescharacteristic
401C4⋊C4—64no—
402C4⋊C4—94no—
403C4⋊C4—94no—
404C4⋊C4—184no—
405C22⋊C4—64no—
406C22⋊C4—94no—
407C22⋊C4—94no—
408C22⋊C4—184no—
409C42—22no—
410C42—34no—
411C42—62no—
412C42—62no—
413C42—94no—
414C42—184no—
415C42—184no—
416C42—182no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—21no—
422C22×C3—62no—
423C22×C3—62no—
424C22×C3—62no—
425C22×C3—122no—
426C22×C3—122no—
427C22×C3C22×C4×D311yescharacteristic
428C22×C3C22×C4×D311yescharacteristic
429C22×C3C2×#23512yes—
430C22×C3C2×#23512yes—
431C22×C3C2×#23711yescharacteristic
432C22×C3C2×#23711yescharacteristic
433C22×C3C2×#23711yescharacteristic
434C22×C3C2×#23911yescharacteristic
435C22×C3D3×#4112yes—
436C22×C3D3×#4112yes—
437C2×D3—22no—
438C2×D3—22no—
439C2×D3—22no—
440C2×D3—42no—
441C2×D3—42no—
442C3×C4—24no—
443C3×C4—44no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—62no—
447C3×C4—62no—
448C3×C4—62no—
449C3×C4—64no—
450C3×C4—64no—
451C3×C4#87714yes—
452C3×C4#89214yes—
453Dic3—22no—
454Dic3—22no—
455Dic3—22no—
456Dic3—24no—
457Dic3—24no—
458Dic3—62no—
459Dic3—62no—
460Dic3—62no—
461Dic3—62no—
462Dic3—122no—
463Dic3—122no—
464Dic3—124no—
465Dic3—122no—
466Dic3—122no—
467C32#229811yescharacteristic, complemented, Sylow
468C23—32no—
469C23—61no—
470C23—62no—
471C23—62no—
472C23—61no—
473C23C22×D3211yescharacteristic
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—32no—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—34no—
481C2×C4—34no—
482C2×C4—62no—
483C2×C4—61no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—61no—
490C2×C4—68no—
491C2×C4—92no—
492C2×C4—92no—
493C2×C4—182no—
494C2×C4—182no—
495C2×C4—182no—
496C2×C4—182no—
497C2×C4—182no—
498C2×C4#379612yes—
499C2×C4C4×D3212yes—
500C2×C4#380512yes—
501C2×C3—21no—
502C2×C3—22no—
503C2×C3—22no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—122no—
507C2×C3C4×#23511yescharacteristic
508C2×C3C4×#23511yescharacteristic
509C2×C3C2×#87711yescharacteristic
510C2×C3C2×#89211yescharacteristic
511C2×C3#552211yescharacteristic
512C2×C3#552211yescharacteristic
513C2×C3#553812yes—
514C2×C3#553812yes—
515C2×C3#555712yes—
516C2×C3#558012yes—
517D3—42no—
518C22—62no—
519C22—62no—
520C22—62no—
521C22—122no—
522C22—122no—
523C22C2×#379611yescharacteristic
524C22C2×C4×D3211yescharacteristic
525C22D3×#23512yes—
526C22D3×#23512yes—
527C22C2×#380511yescharacteristic
528C4—42no—
529C4—62no—
530C4—64no—
531C4—64no—
532C4—62no—
533C4—62no—
534C4—182no—
535C4—182no—
536C4—362no—
537C4#6387814yes—
538C3—21no—
539C3#7344011yescharacteristic, complemented
540C3#7362011yescharacteristic, complemented
541C2—122no—
542C2#1059391112yes—
543C2#1059396511yescharacteristic
544C2#1059396511yescharacteristic
545C2C2×#6387811yescharacteristic
546C2#1059493412yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2298
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592631C2semidirect
4. C3×C4×Dic3⋊C4C2semidirect
5. C4×Dic3⋊Dic3C2semidirect
9. #10591254C2semidirect
10. #10591253C2semidirect
11. C4×Dic32C2semidirect
31. #63855C4semidirect
54. C4×Dic3⋊C4D3semidirect
467. C32#2298semidirect
539. C3#73440semidirect
540. C3#73620semidirect

Maximal subgroups

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

subgroupindex
C2×#638552
#105926312
C3×C4×(C2×D3)⋊C42
C3×C4×Dic3⋊C42
C4×Dic3⋊Dic32
#105912852
#105912842
C4×(C2×D3)⋊Dic32
#105912542
#105912532
C4×Dic322
#736203
#734403