Finite Group Databasebeta

← #11805765

Subgroups — #11805765

Order 1152.

1245 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#625C211yesmaximal, characteristic
2#10592350C211yesmaximal, characteristic, complemented
3C3×#4667C211yesmaximal, characteristic, complemented
4C3×#4666C211yesmaximal, characteristic, complemented
5Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
6#10591363C212yesmaximal
7D3×C3⋊#95C211yesmaximal, characteristic, complemented
8#10591294C211yesmaximal, characteristic, complemented
9#10591285C212yesmaximal, complemented
10#10591252C211yesmaximal, characteristic, complemented
11#10591193C212yesmaximal, complemented
12#73884—31nomaximal
13#73576—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×#625C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2212yes—
23C2×#3724C2211yescharacteristic
24C2×(C2×D3)⋊Dic3C2212yes—
25C2×(C2×D3)⋊Dic3C2211yescharacteristic
26C2×(C2×D3)⋊Dic3C2211yescharacteristic
27C2×Dic32C2212yes—
28C4×#625C418yescomplemented
29C32×#95C2211yescharacteristic
30#63658C2212yes—
31#63658C2211yescharacteristic
32#63658C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2211yescharacteristic
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C4×#67—31no—
39C2×C4×#67—31no—
40C3×#380—31no—
41C3×C4×C22⋊C4—31no—
42#5211—31no—
43C2×C3⋊#95—31no—
44#4990—32no—
45#4978—32no—
46#4958—32no—
47#4956—32no—
48#4944—32no—
49Dic3×C22⋊C4—32no—
50C4×(C2×D3)⋊C4—32no—
51#4933—32no—
52#4667D311yescharacteristic, complemented
53#4666D311yescharacteristic, complemented
54#4664—31no—
55D3×#95—31no—
56#4651—31no—
57#4651—31no—
58#4651—61no—
59#4648—31no—
60#4648—31no—
61C23×C3×D3C2311yescharacteristic
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C2×C3×C4×D3—42no—
73C2×C3×C4×D3—42no—
74C2×C3×C4×D3C2×C414yes—
75C2×C3×C4×D3C2×C414yescomplemented
76C2×#625—22no—
77C2×#625—22no—
78C2×#625C2×C414yes—
79C2×D3×Dic3—24no—
80C2×D3×Dic3—24no—
81C2×D3×Dic3—42no—
82C4×C3⋊Dic3C2×C414yescomplemented
83C3×(C2×D3)⋊C4—24no—
84C3×(C2×D3)⋊C4—24no—
85C3×Dic3⋊C4—42no—
86C3×C4×Dic3—42no—
87#3724C2×C414yescomplemented
88(C2×D3)⋊Dic3—42no—
89(C2×D3)⋊Dic3C2×C414yes—
90(C2×D3)⋊Dic3C2×C414yescomplemented
91Dic32—24no—
92#2353—91noSylow
93C23×C3×C4—31no—
94C23×C3×C4—31no—
95C22×#67—31no—
96C22×#67—31no—
97C23×Dic3—32no—
98C22×C4×D3—32no—
99C22×C4×D3C2×D311yescharacteristic
100C22×C4×D3C2×D311yescharacteristic
101C2×C3×C4⋊C4—32no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C22⋊C4—32no—
104C2×C3×C42—32no—
105C2×#217—31no—
106C2×#217—31no—
107C2×#217—32no—
108C4×#67—38no—
109C4×#67—38no—
110C2×(C2×D3)⋊C4—31no—
111C2×(C2×D3)⋊C4—31no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4C2×D312yes—
114C2×(C2×D3)⋊C4C2×D312yes—
115C2×Dic3⋊C4—31no—
116C2×Dic3⋊C4—31no—
117C2×Dic3⋊C4C2×D312yes—
118C2×C4×Dic3—31no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—61no—
123C2×C4×Dic3C2×D312yes—
124C3×#95—21no—
125C3×#95—31no—
126C3×#95—31no—
127C3×#95C2×D311yescharacteristic
128C3×#95C2×D311yescharacteristic
129C3⋊#95—31no—
130C3⋊#95—31no—
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—61no—
142C3⋊#95—62no—
143C3⋊#95—62no—
144C3⋊#95C2×D311yescharacteristic
145C3⋊#95C2×D311yescharacteristic
146C23×C32C2411yescharacteristic
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—21no—
151C22×C3×D3—21no—
152C22×C3×D3—22no—
153C22×C3×D3C22×C412yes—
154C22×C3×D3C22×C412yes—
155C22×C3×D3#4112yes—
156C22×C3×D3#4112yes—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4C22×C412yes—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3C22×C412yes—
169C2×C3⋊Dic3C22×C412yes—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C22×C412yes—
178C2×C3×Dic3C22×C412yes—
179C2×C3×Dic3#4114yes—
180C3×C4×D3—44no—
181C3×C4×D3—44no—
182#625—28no—
183D3×Dic3—48no—
184C2×C4×D4—91no—
185#388—92no—
186#387—92no—
187#386—92no—
188#383—91no—
189#381—91no—
190#380—31no—
191C4×C22⋊C4—31no—
192C4×C22⋊C4—92no—
193#376—91no—
194C2×#95—91no—
195C24×C3—31no—
196C24×C3—31no—
197C23×D3C22×D311yescharacteristic
198C23×D3C22×D311yescharacteristic
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—32no—
202C22×C3×C4—31no—
203C22×C3×C4—31no—
204C22×C3×C4—34no—
205C22×C3×C4—34no—
206C22×C3×C4—32no—
207C22×C3×C4—122no—
208C22×C3×C4—122no—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D312yes—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C2×#67—34no—
214C2×#67—34no—
215C2×#67—62no—
216C2×#67—62no—
217C2×#67—62no—
218C2×#67—62no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—31no—
223C22×Dic3—32no—
224C22×Dic3—32no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—62no—
228C22×Dic3—64no—
229C22×Dic3—64no—
230C22×Dic3—122no—
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D311yescharacteristic
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D312yes—
235C2×C4×D3—42no—
236C2×C4×D3—42no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—122no—
240C2×C4×D3C4×D314yes—
241C2×C4×D3C4×D314yescomplemented
242C3×C4⋊C4—122no—
243C3×C22⋊C4—64no—
244C3×C22⋊C4—64no—
245C3×C42—122no—
246#217—34no—
247#217—34no—
248#217—122no—
249(C2×D3)⋊C4—24no—
250(C2×D3)⋊C4—24no—
251(C2×D3)⋊C4—34no—
252(C2×D3)⋊C4—34no—
253(C2×D3)⋊C4—122no—
254Dic3⋊C4—34no—
255Dic3⋊C4—34no—
256Dic3⋊C4—42no—
257C4×Dic3—34no—
258C4×Dic3—34no—
259C4×Dic3—42no—
260C4×Dic3—64no—
261C4×Dic3—64no—
262C4×Dic3—64no—
263C22×C32C23×C411yescharacteristic
264C22×C32C2×#4112yes—
265C22×C32C2×#4111yescharacteristic
266C22×C32C2×#4111yescharacteristic
267C22×C32H(5,𝔽2)12yes—
268C2×C3×D3—22no—
269C2×C3×D3—22no—
270C2×C3×D3—24no—
271C2×C3×D3—24no—
272C2×C3×D3—22no—
273C2×C3×D3—22no—
274C2×C3×D3—22no—
275C2×C3×D3—42no—
276C2×C3×D3—42no—
277C2×C3×D3#11714yes—
278C32×C4—22no—
279C32×C4—42no—
280C3⋊Dic3—22no—
281C3⋊Dic3—22no—
282C3⋊Dic3—42no—
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—24no—
286C3×Dic3—42no—
287C22×D4—91no—
288C23×C4—31no—
289C23×C4—31no—
290C23×C4—92no—
291C4×D4—98no—
292C2×C4⋊C4—32no—
293C2×C4⋊C4—91no—
294C2×C22⋊C4—32no—
295C2×C22⋊C4—32no—
296C2×C22⋊C4—91no—
297C2×C22⋊C4—91no—
298C2×C22⋊C4—92no—
299C2×C42—32no—
300C2×C42—91no—
301C2×C42—92no—
302#95—31no—
303#95—31no—
304#95—92no—
305#95—92no—
306#95—92no—
307#95—91no—
308#95—92no—
309#95—92no—
310#95D3211yescharacteristic
311C23×C3—21no—
312C23×C3—32no—
313C23×C3—32no—
314C23×C3—32no—
315C23×C3—32no—
316C23×C3—62no—
317C23×C3—62no—
318C23×C3—61no—
319C23×C3—62no—
320C23×C3—61no—
321C23×C3—62no—
322C23×C3C23×D311yescharacteristic
323C23×C3C23×D311yescharacteristic
324C22×D3—22no—
325C22×D3—22no—
326C22×D3—22no—
327C22×D3—22no—
328C22×D3—21no—
329C22×D3—21no—
330C22×D3C2×C4×D312yes—
331C22×D3C2×C4×D312yes—
332C22×D3#23712yes—
333C22×D3#23912yes—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—34no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—124no—
358C2×C3×C4—124no—
359C2×C3×C4C2×C4×D312yes—
360C2×C3×C4C2×C4×D312yes—
361#67—68no—
362#67—68no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—32no—
371C2×Dic3—32no—
372C2×Dic3—32no—
373C2×Dic3—32no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—62no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—122no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3—122no—
392C2×Dic3—122no—
393C2×Dic3—122no—
394C2×Dic3—128no—
395C2×Dic3C2×C4×D312yes—
396C2×Dic3C2×C4×D312yes—
397C2×Dic3#23514yes—
398C4×D3—44no—
399C4×D3—44no—
400C4×D3—128no—
401C2×C32C2×#11711yescharacteristic
402C2×C32C4×#4111yescharacteristic
403C2×C32#51811yescharacteristic
404C2×C32#55112yes—
405C2×C32#55312yes—
406C3×D3—24no—
407C3×D3—42no—
408C24—31no—
409C24—31no—
410C2×D4—94no—
411C2×D4—182no—
412C2×D4—182no—
413C22×C4—32no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—34no—
417C22×C4—34no—
418C22×C4—32no—
419C22×C4—91no—
420C22×C4—91no—
421C22×C4—92no—
422C22×C4—122no—
423C22×C4—122no—
424C22×C4—184no—
425C22×C4—184no—
426C22×C4—362no—
427C22×C4C2×D3212yes—
428C22×C4C2×D3211yescharacteristic
429C4⋊C4—94no—
430C4⋊C4—122no—
431C22⋊C4—64no—
432C22⋊C4—64no—
433C22⋊C4—94no—
434C22⋊C4—94no—
435C22⋊C4—362no—
436C42—94no—
437C42—122no—
438C42—184no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—34no—
445C22×C3—62no—
446C22×C3—62no—
447C22×C3—64no—
448C22×C3—64no—
449C22×C3—62no—
450C22×C3—62no—
451C22×C3—62no—
452C22×C3—122no—
453C22×C3—122no—
454C22×C3C22×C4×D311yescharacteristic
455C22×C3C22×C4×D311yescharacteristic
456C22×C3C2×#23512yes—
457C22×C3C2×#23711yescharacteristic
458C22×C3#100412yes—
459C22×C3#100412yes—
460C22×C3C2×#23911yescharacteristic
461C22×C3D3×#4112yes—
462C22×C3D3×#4111yescharacteristic
463C22×C3D3×#4111yescharacteristic
464C2×D3—24no—
465C2×D3—22no—
466C2×D3—22no—
467C2×D3—24no—
468C2×D3—22no—
469C2×D3—22no—
470C2×D3—22no—
471C2×D3—42no—
472C2×D3—42no—
473C2×D3#89214yes—
474C3×C4—22no—
475C3×C4—22no—
476C3×C4—42no—
477C3×C4—42no—
478C3×C4—42no—
479C3×C4—64no—
480C3×C4—62no—
481C3×C4—62no—
482C3×C4—82no—
483C3×C4—122no—
484Dic3—22no—
485Dic3—22no—
486Dic3—24no—
487Dic3—42no—
488Dic3—62no—
489Dic3—62no—
490Dic3—62no—
491Dic3—62no—
492Dic3—122no—
493Dic3—122no—
494Dic3—122no—
495Dic3—122no—
496Dic3—242no—
497C32#235311yescharacteristic, complemented, Sylow
498C23—32no—
499C23—32no—
500C23—32no—
501C23—32no—
502C23—62no—
503C23—62no—
504C23—62no—
505C23—61no—
506C23—62no—
507C23—61no—
508C23C22×D3211yescharacteristic
509D4—188no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—32no—
515C2×C4—32no—
516C2×C4—34no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—92no—
525C2×C4—92no—
526C2×C4—124no—
527C2×C4—124no—
528C2×C4—182no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—182no—
532C2×C4—182no—
533C2×C4—182no—
534C2×C4—368no—
535C2×C4C4×D3212yes—
536C2×C3—21no—
537C2×C3—22no—
538C2×C3—22no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—64no—
542C2×C3—122no—
543C2×C3C4×#23511yescharacteristic
544C2×C3#548611yescharacteristic
545C2×C3#548611yescharacteristic
546C2×C3C2×#89211yescharacteristic
547C2×C3D3×#11711yescharacteristic
548C2×C3#552211yescharacteristic
549C2×C3#555612yes—
550C2×C3#555812yes—
551C2×C3#560112yes—
552C2×C3#563712yes—
553D3—24no—
554D3—42no—
555C22—34no—
556C22—64no—
557C22—64no—
558C22—62no—
559C22—62no—
560C22—62no—
561C22—62no—
562C22—62no—
563C22—122no—
564C22—122no—
565C22C2×C4×D3211yescharacteristic
566C22D3×#23512yes—
567C22D3×#23711yescharacteristic
568C22#6431312yes—
569C22D3×#23911yescharacteristic
570C4—22no—
571C4—42no—
572C4—64no—
573C4—62no—
574C4—62no—
575C4—122no—
576C4—182no—
577C4—182no—
578C4—362no—
579C3—21no—
580C3#7357611yescharacteristic, complemented
581C3#7388411yescharacteristic, complemented
582C2—64no—
583C2—122no—
584C2#1059396511yescharacteristic
585C2#1059409612yes—
586C2#1059418111yescharacteristic
587C2D3×#89211yescharacteristic
588C2#1059464212yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
hypercenter#95D32
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592350C2semidirect
3. C3×#4667C2semidirect
4. C3×#4666C2semidirect
5. Dic3×(C2×D3)⋊C4C2semidirect
7. D3×C3⋊#95C2semidirect
8. #10591294C2semidirect
9. #10591285C2semidirect
10. #10591252C2semidirect
11. #10591193C2semidirect
28. C4×#625C4semidirect
52. #4667D3semidirect
53. #4666D3semidirect
75. C2×C3×C4×D3C2×C4semidirect
82. C4×C3⋊Dic3C2×C4semidirect
87. #3724C2×C4semidirect
90. (C2×D3)⋊Dic3C2×C4semidirect
241. C2×C4×D3C4×D3semidirect
497. C32#2353semidirect
580. C3#73576semidirect
581. C3#73884semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6252
#105923502
C3×#46672
C3×#46662
Dic3×(C2×D3)⋊C42
#105913632
D3×C3⋊#952
#105912942
#105912852
#105912522
#105911932
#738843
#735763