Finite Group Databasebeta

← #11808518

Subgroups — #11808518

Order 1152.

1373 conjugacy classes of subgroups.

The subgroup lattice has 575 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63883C211yesmaximal, characteristic
2C2×#63883C211yesmaximal, characteristic
3C3⋊D3×#95C211yesmaximal, characteristic
4C3×#4658C212yesmaximal, complemented
5#10591370C211yesmaximal, characteristic
6#10591370C211yesmaximal, characteristic
7#10591370C211yesmaximal, characteristic
8#10591370C211yesmaximal, characteristic
9#10591341C212yesmaximal, complemented
10#10591207C212yesmaximal, complemented
11#10591196C212yesmaximal, complemented
12D3×#400—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#624C2211yescharacteristic
17C22×#624C2211yescharacteristic
18C22×#624C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×Dic3⋊Dic3C2212yes—
23C2×Dic3⋊Dic3C2212yes—
24#63883—24no—
25#63883—24no—
26C32×#95C2211yescharacteristic
27#63658C2211yescharacteristic
28#63658C2211yescharacteristic
29#63658C2211yescharacteristic
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×D3×C4⋊C4—32no—
39C2×D3×C4⋊C4—32no—
40C3×#400—32no—
41#4986—32no—
42#4985—32no—
43D3×#95—32no—
44D3×#95—32no—
45D3×#95—32no—
46D3×#95—32no—
47D3×#95—32no—
48D3×#95—61no—
49#4660—32no—
50#4660—32no—
51#4659—32no—
52#4658—32no—
53#4658D312yescomplemented
54C23×C3⋊D3C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—22no—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C2×#624—22no—
75C2×#624—22no—
76C2×#624—22no—
77C2×#624—22no—
78C2×#624—22no—
79C2×#624—22no—
80C2×#624—22no—
81C2×#624—22no—
82C2×#624—22no—
83C2×#624—22no—
84C2×#624D414yes—
85C2×#624Q814yes—
86C3×Dic3⋊C4—24no—
87C3×Dic3⋊C4—24no—
88Dic3⋊Dic3—24no—
89Dic3⋊Dic3—24no—
90C2×#400—91noSylow
91C22×C4×D3—32no—
92C22×C4×D3—32no—
93C22×C4×D3—32no—
94C22×C4×D3—32no—
95C22×C4×D3—32no—
96C22×C4×D3—32no—
97C22×C4×D3—32no—
98C22×C4×D3—61no—
99C22×C4×D3—61no—
100C22×C4×D3—61no—
101C2×C3×C4⋊C4—32no—
102C2×C3×C4⋊C4—32no—
103C2×C4⋊Dic3—32no—
104C2×C4⋊Dic3—32no—
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—32no—
107C2×Dic3⋊C4C2×D312yes—
108C2×Dic3⋊C4C2×D312yes—
109D3×C4⋊C4—68no—
110D3×C4⋊C4—68no—
111C3×#95—21no—
112C3×#95—32no—
113C3×#95—32no—
114C3×#95—32no—
115C3×#95—32no—
116C3×#95C2×D312yes—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C3⋊#95—61no—
129C3⋊#95—61no—
130C3⋊#95—61no—
131C3⋊#95C2×D312yes—
132C3⋊#95C2×D312yes—
133C3⋊#95C2×D312yes—
134C3⋊#95C2×D312yes—
135C23×C32C2411yescharacteristic
136C22×C3⋊D3C2×D412yes—
137C22×C3⋊D3C2×Q812yes—
138C22×C3⋊D3#4112yes—
139C22×C3⋊D3#4112yes—
140C22×C3⋊D3#4112yes—
141C22×C3⋊D3#4112yes—
142C22×C3⋊D3#4112yes—
143C2×C32×C4—21no—
144C2×C32×C4—21no—
145C2×C32×C4—21no—
146C2×C32×C4—21no—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C4×C3⋊D3—44no—
162C4×C3⋊D3—44no—
163C4×C3⋊D3—44no—
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—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3C2×D414yes—
175C2×C3×Dic3C2×Q814yes—
176#624—28no—
177#624—28no—
178#624—44no—
179#624—44no—
180C22×C4⋊C4—91no—
181C22×C4⋊C4—91no—
182#400—32no—
183#400—92no—
184#400—92no—
185#400—92no—
186C2×#95—91no—
187C2×#95—91no—
188C2×#95—91no—
189C2×#95—91no—
190C2×#95—91no—
191C23×D3—32no—
192C23×D3—61no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4C22×D312yes—
201C22×C3×C4C22×D312yes—
202C22×C3×C4C22×D312yes—
203C22×Dic3—32no—
204C22×Dic3—32no—
205C22×Dic3—32no—
206C22×Dic3—61no—
207C22×Dic3—61no—
208C22×Dic3—61no—
209C22×Dic3C22×D312yes—
210C22×Dic3C22×D312yes—
211C22×Dic3C22×D312yes—
212C22×Dic3C22×D312yes—
213C2×C4×D3—38no—
214C2×C4×D3—38no—
215C2×C4×D3—64no—
216C2×C4×D3—64no—
217C2×C4×D3—64no—
218C2×C4×D3—64no—
219C2×C4×D3—64no—
220C2×C4×D3—64no—
221C2×C4×D3—64no—
222C2×C4×D3—64no—
223C2×C4×D3—64no—
224C2×C4×D3—64no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—64no—
232C2×C4×D3—64no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—122no—
238C2×C4×D3—122no—
239C2×C4×D3—122no—
240C2×C4×D3—122no—
241C2×C4×D3—122no—
242C2×C4×D3—122no—
243C3×C4⋊C4—64no—
244C3×C4⋊C4—64no—
245C4⋊Dic3—64no—
246C4⋊Dic3—64no—
247Dic3⋊C4—24no—
248Dic3⋊C4—24no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251C22×C32C22×D411yescharacteristic
252C22×C32C22×Q811yescharacteristic
253C22×C32C2×#4111yescharacteristic
254C22×C32C2×#4111yescharacteristic
255C22×C32C2×#4111yescharacteristic
256C22×C32C2×#4111yescharacteristic
257C22×C32C2×#4111yescharacteristic
258C2×C3⋊D3C22⋊Q814yes—
259C2×C3⋊D3#12314yes—
260C2×C3⋊D3#12414yes—
261C2×C3⋊D3#12514yes—
262C2×C3⋊D3#12514yes—
263C2×C3⋊D3#12614yes—
264C2×C3⋊D3#12614yes—
265C32×C4—41no—
266C32×C4—41no—
267C32×C4—41no—
268C3⋊Dic3—41no—
269C3⋊Dic3—41no—
270C3⋊Dic3—41no—
271C3×Dic3—24no—
272C3×Dic3—24no—
273C3×Dic3—42no—
274C3×Dic3—42no—
275C23×C4—91no—
276C23×C4—91no—
277C23×C4—91no—
278C23×C4—91no—
279C23×C4—91no—
280C23×C4—91no—
281C23×C4—91no—
282C2×C4⋊C4—32no—
283C2×C4⋊C4—32no—
284C2×C4⋊C4—92no—
285C2×C4⋊C4—92no—
286C2×C4⋊C4—184no—
287C2×C4⋊C4—184no—
288#95—32no—
289#95—32no—
290#95—32no—
291#95—32no—
292#95—92no—
293#95—92no—
294#95—92no—
295#95—92no—
296#95—91no—
297#95—91no—
298#95—91no—
299#95D3211yescharacteristic
300C23×C3—21no—
301C23×C3C23×D312yes—
302C22×D3—34no—
303C22×D3—34no—
304C22×D3—34no—
305C22×D3—34no—
306C22×D3—34no—
307C22×D3—34no—
308C22×D3—34no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—62no—
314C22×D3—62no—
315C22×D3—62no—
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—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—34no—
329C2×C3×C4—34no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—121no—
369C2×Dic3—121no—
370C2×Dic3—121no—
371C2×Dic3—121no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374C2×Dic3D3×D414yes—
375C2×Dic3D3×Q814yes—
376C4×D3—616no—
377C4×D3—616no—
378C4×D3—128no—
379C4×D3—128no—
380C4×D3—128no—
381C4×D3—128no—
382C4×D3—128no—
383C4×D3—128no—
384C4×D3—128no—
385C4×D3—128no—
386C2×C32C2×C22⋊Q811yescharacteristic
387C2×C32C2×#12311yescharacteristic
388C2×C32C2×#12411yescharacteristic
389C2×C32C2×#12511yescharacteristic
390C2×C32C2×#12511yescharacteristic
391C2×C32C2×#12611yescharacteristic
392C2×C32C2×#12611yescharacteristic
393C3⋊D3#40018yescomplemented
394C24—91no—
395C22×C4—32no—
396C22×C4—32no—
397C22×C4—32no—
398C22×C4—32no—
399C22×C4—94no—
400C22×C4—94no—
401C22×C4—91no—
402C22×C4—91no—
403C22×C4—91no—
404C22×C4—182no—
405C22×C4—182no—
406C22×C4—182no—
407C22×C4—182no—
408C22×C4—182no—
409C22×C4—182no—
410C22×C4—182no—
411C22×C4—182no—
412C22×C4—182no—
413C22×C4—182no—
414C22×C4—182no—
415C22×C4—182no—
416C22×C4—182no—
417C22×C4—182no—
418C22×C4—182no—
419C22×C4—182no—
420C22×C4—182no—
421C22×C4—182no—
422C22×C4—182no—
423C22×C4C2×D3211yescharacteristic
424C22×C4C2×D3211yescharacteristic
425C22×C4C2×D3211yescharacteristic
426C4⋊C4—64no—
427C4⋊C4—64no—
428C4⋊C4—184no—
429C4⋊C4—184no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3C2×D3×D412yes—
438C22×C3C2×D3×Q812yes—
439C22×C3D3×#4112yes—
440C22×C3D3×#4112yes—
441C22×C3D3×#4112yes—
442C22×C3D3×#4112yes—
443C22×C3D3×#4112yes—
444C2×D3—38no—
445C2×D3—38no—
446C2×D3—38no—
447C2×D3—38no—
448C2×D3—38no—
449C2×D3—38no—
450C2×D3—38no—
451C2×D3—64no—
452C2×D3—64no—
453C2×D3—64no—
454C2×D3—64no—
455C2×D3—64no—
456C2×D3—64no—
457C2×D3—64no—
458C3×C4—42no—
459C3×C4—42no—
460C3×C4—42no—
461C3×C4—42no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4—64no—
465C3×C4—64no—
466C3×C4—122no—
467C3×C4—122no—
468Dic3—24no—
469Dic3—24no—
470Dic3—42no—
471Dic3—42no—
472Dic3—122no—
473Dic3—122no—
474Dic3—122no—
475Dic3—122no—
476Dic3—122no—
477Dic3—122no—
478C32C2×#40011yescharacteristic, complemented, Sylow
479C23—92no—
480C23—92no—
481C23—92no—
482C23—92no—
483C23—92no—
484C23—92no—
485C23—92no—
486C23C22×D3211yescharacteristic
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—34no—
497C2×C4—34no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—188no—
509C2×C4—188no—
510C2×C4—181no—
511C2×C4—181no—
512C2×C4—181no—
513C2×C4—181no—
514C2×C4—181no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—181no—
519C2×C4—364no—
520C2×C4—364no—
521C2×C4—364no—
522C2×C4—364no—
523C2×C4—364no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3D3×C22⋊Q812yes—
532C2×C3D3×#12312yes—
533C2×C3D3×#12412yes—
534C2×C3D3×#12512yes—
535C2×C3D3×#12512yes—
536C2×C3D3×#12612yes—
537C2×C3D3×#12612yes—
538D3—316no—
539D3—68no—
540C22—94no—
541C22—94no—
542C22—94no—
543C22—94no—
544C22—94no—
545C22—94no—
546C22—94no—
547C22#6430611yescharacteristic
548C22#6430611yescharacteristic
549C22#6430611yescharacteristic
550C22D32×D411yescharacteristic
551C22#6431211yescharacteristic
552C22#6431211yescharacteristic
553C22D32×Q811yescharacteristic
554C4—41no—
555C4—41no—
556C4—41no—
557C4—64no—
558C4—64no—
559C4—122no—
560C4—122no—
561C4—361no—
562C4—361no—
563C4—361no—
564C3—21no—
565C3D3×#40012yescomplemented
566C2—98no—
567C2#1059402011yescharacteristic
568C2#1059415411yescharacteristic
569C2#1059426011yescharacteristic
570C2#1059428811yescharacteristic
571C2#1059439911yescharacteristic
572C2#1059439911yescharacteristic
573C2#1059462411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32C2×#400
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C3×#4658C2semidirect
9. #10591341C2semidirect
10. #10591207C2semidirect
11. #10591196C2semidirect
53. #4658D3semidirect
393. C3⋊D3#400semidirect
478. C32C2×#400semidirect
565. C3D3×#400semidirect

Maximal subgroups

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

subgroupindex
C2×#638832
C3⋊D3×#952
C3×#46582
#105913702
#105913412
#105912072
#105911962
D3×#4003