Finite Group Databasebeta

← #11801509

Subgroups — #11801509

Order 1152.

1605 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic
2C22×Dic32C211yesmaximal, characteristic, complemented
3C2×#63849C211yesmaximal, characteristic, complemented
4C3×#4950C212yesmaximal, complemented
5#10591711C212yesmaximal
6#10591705C211yesmaximal, characteristic, complemented
7#10591274C211yesmaximal, characteristic, complemented
8#10591266C212yesmaximal, complemented
9#10591263C212yesmaximal, complemented
10#10591260C211yesmaximal, characteristic, complemented
11#10591252C211yesmaximal, characteristic, complemented
12#74377—32nomaximal
13C22×#638C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C23×C3×Dic3C2212yes—
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×#3752C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21#64090C418yescomplemented
22C2×C3×#217C2212yes—
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×C4⋊Dic3C2212yes—
25C2×#3722C2212yes—
26C2×#3722C2212yes—
27C2×Dic32—24no—
28C2×Dic32C2211yescharacteristic
29C2×Dic32C2211yescharacteristic
30C2×Dic32C2211yescharacteristic
31C2×Dic32C2212yes—
32C2×Dic32C2211yescharacteristic
33#63849—24no—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C22×C4×Dic3—32no—
40C2×#892—32no—
41C2×#67⋊C4—32no—
42C2×#67⋊C4—61no—
43C3×#385—32no—
44#5213—32no—
45#4990—32no—
46#4978—32no—
47Dic3×C4⋊C4—32no—
48#4958—32no—
49#4950D312yescomplemented
50Dic3×C22⋊C4—32no—
51#4670—32no—
52#4666—32no—
53#4655—32no—
54#4648—32no—
55C24×C32C2311yescharacteristic
56C23×C3⋊D3C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C2×#638—24no—
60C2×#638C2×C414yes—
61C22×C3⋊Dic3—22no—
62C22×C3⋊Dic3—22no—
63C22×C3⋊Dic3C2×C414yes—
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3C2×C414yescomplemented
70C22×C3×Dic3—24no—
71C22×C3×Dic3—24no—
72C22×C3×Dic3—24no—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C32×C22⋊C4C2×C414yes—
78#3752C2×C414yescomplemented
79#3750C2×C414yescomplemented
80C4×C3⋊Dic3C2×C414yescomplemented
81C3×#217—24no—
82C3×C4⋊Dic3—24no—
83C3×C4⋊Dic3—24no—
84#3722—24no—
85#3722—24no—
86Dic32—22no—
87Dic32—22no—
88Dic32—22no—
89Dic32—24no—
90Dic32D414yescomplemented
91#2290—91noSylow
92C23×C3×C4—32no—
93C22×#67—32no—
94C22×#67—61no—
95C23×Dic3—32no—
96C23×Dic3—61no—
97C23×Dic3C2×D312yes—
98C22×C4×D3—32no—
99C22×C4×D3—61no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C4⋊C4—32no—
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—32no—
104C2×C3×C22⋊C4C2×D312yes—
105C2×#217C2×D312yes—
106C2×(C2×D3)⋊C4—32no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—61no—
112C2×C4⋊Dic3C2×D312yes—
113C2×C4⋊Dic3C2×D312yes—
114C2×Dic3⋊C4—32no—
115C2×Dic3⋊C4—61no—
116C2×C4×Dic3—32no—
117C2×C4×Dic3—32no—
118C2×C4×Dic3—32no—
119C2×C4×Dic3—32no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—61no—
124C2×C4×Dic3—68no—
125#892—68no—
126#67⋊C4—316no—
127#67⋊C4—68no—
128C3×#95—32no—
129C3×#95—32no—
130C3⋊#95—32no—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95C2×D312yes—
137C3⋊#95C2×D312yes—
138C23×C32—21no—
139C23×C32—22no—
140C23×C32—21no—
141C23×C32C22×C412yes—
142C23×C32#4114yes—
143C23×C32C2411yescharacteristic
144C22×C3⋊D3—22no—
145C22×C3⋊D3—21no—
146C22×C3⋊D3—22no—
147C22×C3⋊D3—21no—
148C22×C3⋊D3C22×C412yes—
149C2×C32×C4—21no—
150C2×C32×C4—22no—
151C2×C32×C4—21no—
152C2×C32×C4C22×C412yes—
153C2×C32×C4C22×C412yes—
154#638—28no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—28no—
159C2×C3⋊Dic3C22×C412yes—
160C2×C3⋊Dic3C22×C412yes—
161C2×C3⋊Dic3C22×C412yes—
162C2×C3⋊Dic3C2×D412yes—
163C2×C3⋊Dic3#4112yes—
164C4×C3⋊D3—28no—
165C2×C3×Dic3—216no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
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×Dic3C2×D414yes—
177C2×C3×Dic3#4114yes—
178C2×C4×D4—91no—
179C2×#117—91no—
180C22×C42—91no—
181#388—92no—
182#387—92no—
183#386—92no—
184#385—32no—
185C4×C4⋊C4—91no—
186C4×C22⋊C4—91no—
187C4×C22⋊C4—91no—
188#376—91no—
189C24×C3—21no—
190C24×C3C22×D312yes—
191C23×D3—32no—
192C23×D3—61no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—32no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—64no—
200C22×C3×C4—64no—
201C22×C3×C4—64no—
202C22×C3×C4C22×D312yes—
203C22×C3×C4C22×D312yes—
204C2×#67—38no—
205C2×#67—64no—
206C2×#67—68no—
207C2×#67—64no—
208C2×#67—64no—
209C22×Dic3—24no—
210C22×Dic3—24no—
211C22×Dic3—24no—
212C22×Dic3—32no—
213C22×Dic3—38no—
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C22×Dic3—64no—
219C22×Dic3—61no—
220C22×Dic3—64no—
221C22×Dic3—64no—
222C22×Dic3—122no—
223C22×Dic3—122no—
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D312yes—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D312yes—
228C2×C4×D3—38no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—64no—
232C2×C4×D3—122no—
233C2×C4×D3—122no—
234C3×C4⋊C4—64no—
235C3×C4⋊C4—64no—
236C3×C22⋊C4—24no—
237C3×C22⋊C4—64no—
238C3×C22⋊C4C4×D318yes—
239#217—24no—
240(C2×D3)⋊C4—38no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246C4⋊Dic3—24no—
247C4⋊Dic3—24no—
248Dic3⋊C4—38no—
249Dic3⋊C4—64no—
250C4×Dic3—38no—
251C4×Dic3—38no—
252C4×Dic3—64no—
253C4×Dic3—64no—
254C4×Dic3—64no—
255C4×Dic3—64no—
256C4×Dic3—64no—
257C4×Dic3—64no—
258C22×C32—22no—
259C22×C32—22no—
260C22×C32—24no—
261C22×C32—24no—
262C22×C32#11714yescomplemented
263C22×C32C23×C411yescharacteristic
264C22×C32C22×D411yescharacteristic
265C22×C32C2×#4112yes—
266C22×C32C2×#4112yes—
267C22×C32C2×#4111yescharacteristic
268C2×C3⋊D3—22no—
269C2×C3⋊D3—22no—
270C2×C3⋊D3—22no—
271C2×C3⋊D3—42no—
272C2×C3⋊D3—42no—
273C32×C4—22no—
274C32×C4—22no—
275C3⋊Dic3—22no—
276C3⋊Dic3—22no—
277C3⋊Dic3C4×D414yes—
278C3×Dic3—24no—
279C3×Dic3—24no—
280C3×Dic3—42no—
281C3×Dic3—42no—
282C22×D4—91no—
283C23×C4—32no—
284C23×C4—91no—
285C23×C4—91no—
286C4×D4—98no—
287#117—184no—
288C2×C4⋊C4—32no—
289C2×C4⋊C4—32no—
290C2×C4⋊C4—91no—
291C2×C22⋊C4—32no—
292C2×C22⋊C4—91no—
293C2×C22⋊C4—92no—
294C2×C22⋊C4—92no—
295C2×C22⋊C4D3211yescharacteristic
296C2×C42—91no—
297C2×C42—91no—
298C2×C42—91no—
299C2×C42—91no—
300C2×C42—91no—
301C2×C42—92no—
302C2×C42—184no—
303#95—32no—
304#95—32no—
305#95—92no—
306#95—92no—
307#95—92no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—22no—
312C23×C3—21no—
313C23×C3—24no—
314C23×C3—22no—
315C23×C3—41no—
316C23×C3—41no—
317C23×C3—42no—
318C23×C3C2×C4×D314yes—
319C23×C3#23714yes—
320C23×C3#23914yes—
321C23×C3C23×D312yes—
322C22×D3—34no—
323C22×D3—62no—
324C22×D3—64no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—121no—
332C22×D3—121no—
333C22×D3—122no—
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—34no—
341C2×C3×C4—34no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—42no—
345C2×C3×C4—616no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
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×C4C2×C4×D314yes—
357C2×C3×C4C2×C4×D314yes—
358#67—616no—
359#67—616no—
360C2×Dic3—216no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—34no—
374C2×Dic3—34no—
375C2×Dic3—34no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—616no—
382C2×Dic3—64no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—128no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C2×Dic3D3×D414yes—
391C2×Dic3#23714yes—
392C4×D3—616no—
393C4×D3—128no—
394C2×C32—24no—
395C2×C32C2×#11711yescharacteristic
396C2×C32C2×C4×D411yescharacteristic
397C2×C32C4×#4111yescharacteristic
398C2×C32#52512yes—
399C2×C32#52912yes—
400C3⋊D3—42no—
401C24—91no—
402C24C2×D3211yescharacteristic
403C2×D4—94no—
404C2×D4—184no—
405C22×C4—32no—
406C22×C4—32no—
407C22×C4—32no—
408C22×C4—32no—
409C22×C4—64no—
410C22×C4—64no—
411C22×C4—64no—
412C22×C4—91no—
413C22×C4—91no—
414C22×C4—91no—
415C22×C4—94no—
416C22×C4—94no—
417C22×C4—182no—
418C22×C4—182no—
419C22×C4—182no—
420C22×C4—182no—
421C22×C4C2×D3211yescharacteristic
422C22×C4C2×D3211yescharacteristic
423C4⋊C4—64no—
424C4⋊C4—64no—
425C4⋊C4—94no—
426C22⋊C4—64no—
427C22⋊C4—94no—
428C22⋊C4—184no—
429C22⋊C4—184no—
430C22⋊C4#62414yes—
431C42—94no—
432C42—94no—
433C42—184no—
434C42—182no—
435C42—182no—
436C42—182no—
437C22×C3—24no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3—24no—
443C22×C3—22no—
444C22×C3—21no—
445C22×C3—22no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—24no—
449C22×C3—42no—
450C22×C3—44no—
451C22×C3—44no—
452C22×C3—42no—
453C22×C3#89218yescomplemented
454C22×C3C22×C4×D312yes—
455C22×C3C2×D3×D412yes—
456C22×C3C2×#23712yes—
457C22×C3C2×#23712yes—
458C22×C3C2×#23912yes—
459C22×C3D3×#4112yes—
460C22×C3D3×#4112yes—
461C2×D3—64no—
462C2×D3—64no—
463C2×D3—64no—
464C2×D3—64no—
465C2×D3—122no—
466C2×D3—122no—
467C2×D3—124no—
468C2×D3—124no—
469C2×D3—122no—
470C2×D3—122no—
471C2×D3—122no—
472C2×D3—122no—
473C3×C4—24no—
474C3×C4—24no—
475C3×C4—42no—
476C3×C4—42no—
477C3×C4—64no—
478C3×C4—64no—
479C3×C4—122no—
480C3×C4—122no—
481Dic3—24no—
482Dic3—24no—
483Dic3—38no—
484Dic3—42no—
485Dic3—42no—
486Dic3—64no—
487Dic3—64no—
488Dic3—64no—
489Dic3—64no—
490Dic3—122no—
491C32#229011yescharacteristic, complemented, Sylow
492C23—21no—
493C23—22no—
494C23—21no—
495C23—92no—
496C23—182no—
497C23—181no—
498C23—182no—
499C23—181no—
500C23#379614yes—
501C23C2×#62412yes—
502C23C22×D3211yescharacteristic
503D4—188no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—34no—
508C2×C4—34no—
509C2×C4—616no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—92no—
521C2×C4—92no—
522C2×C4—92no—
523C2×C4—92no—
524C2×C4—92no—
525C2×C4—188no—
526C2×C4—188no—
527C2×C4—182no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4C2×#62412yes—
531C2×C4C2×#62412yes—
532C2×C3—28no—
533C2×C3—22no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—22no—
537C2×C3—21no—
538C2×C3—44no—
539C2×C3C2×#89212yes—
540C2×C3C4×#23712yes—
541C2×C3C4×D3×D412yes—
542C2×C3#558612yes—
543C2×C3#562412yes—
544C2×C3#562712yes—
545C2×C3#564912yes—
546D3—124no—
547D3—124no—
548C22—24no—
549C22—22no—
550C22—24no—
551C22—22no—
552C22—182no—
553C22—182no—
554C22—182no—
555C22—362no—
556C22—362no—
557C22#6384914yescomplemented
558C22C2×#379612yes—
559C22D32×D411yescharacteristic
560C22D3×#23712yes—
561C22#6431211yescharacteristic
562C22C22×#62411yescharacteristic
563C4—22no—
564C4—22no—
565C4—64no—
566C4—64no—
567C4—94no—
568C4—122no—
569C4—122no—
570C4—182no—
571C4—182no—
572C3—21no—
573C3#7437712yescomplemented
574C2—24no—
575C2—362no—
576C2#1059405512yes—
577C2#1059414412yes—
578C2C2×#6384911yescharacteristic
579C2D4×#62411yescharacteristic
580C2#1059519011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2290
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×Dic32C2semidirect
3. C2×#63849C2semidirect
4. C3×#4950C2semidirect
6. #10591705C2semidirect
7. #10591274C2semidirect
8. #10591266C2semidirect
9. #10591263C2semidirect
10. #10591260C2semidirect
11. #10591252C2semidirect
21. #64090C4semidirect
49. #4950D3semidirect
69. C2×C4×C3⋊D3C2×C4semidirect
78. #3752C2×C4semidirect
79. #3750C2×C4semidirect
80. C4×C3⋊Dic3C2×C4semidirect
90. Dic32D4semidirect
262. C22×C32#117semidirect
453. C22×C3#892semidirect
491. C32#2290semidirect
557. C22#63849semidirect
573. C3#74377semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
C22×Dic322
C2×#638492
C3×#49502
#105917112
#105917052
#105912742
#105912662
#105912632
#105912602
#105912522
#743773